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Probability Distribution One Mark Questions. Choose the Correct Answer 1.If f(x) = kx 2, 0 < x < 3 0, elsewhere is a probability density function then.

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Presentation on theme: "Probability Distribution One Mark Questions. Choose the Correct Answer 1.If f(x) = kx 2, 0 < x < 3 0, elsewhere is a probability density function then."— Presentation transcript:

1 Probability Distribution One Mark Questions

2 Choose the Correct Answer 1.If f(x) = kx 2, 0 < x < 3 0, elsewhere is a probability density function then the value of k is (a) 1/3 (b) 1/6 (c) 1/9 (d) 1/12 2.If f(x) = –  < x <  is a p.d.f of a continuous random variable X, then the value of A is (a) 16 (b) 8 (c) 4 (d) 1

3 Choose the Correct Answer 3.A random variable X has the following probability distribution X P(X = x) ¼ 2a3a4a5a¼ then P(1  X  4) (a) 10/21(b) 2/7 (c) 1/14 (d) 1/2

4 Choose the Correct Answer 4.A random variable X has the following probability mass function as follows: X-231 P(X = x) /6 /4 /12 then the value of is (a) 1(b) 2 (c) 3 (d) 4

5 Choose the Correct Answer 5.A random variable X has the following p.d.f then the value of is (a) (b) (c) (d) –1 or X P(X = x) 0k2k 3kk2k2 2 k 2 7k 2 +k

6 Choose the Correct Answer 6.X is a discrete random variable which takes 0, 1, 2 and P(X = 0) = P(X = 1) = then the value of P(X = 2)is (a) (b) (c) (d)

7 Choose The Correct Answer 7.Given E(X + c) = 8 and E(X – c) = 12 then the value of c is (a) – 2 (b) 4 (c) – 4 (d) 2 8.X is a random variable taking the value 3, 4 and 7 with probabilities 1/3, ¼ and 4/7 then E(X) is (a) 5 (b) 6 (c) 7 (d) 3

8 Choose The Correct Answer 9.Variance of the random variable X is 4. Its mean is 2, then E(X 2 ) is (a) 2 (b) 4 (c) 6 (d)  2 = 20,  2 ’ = 276 for a discrete random variable X, then the mean of the random variable X is (a) 16 (b) 5 (c) 2 (d) 1

9 Choose The Correct Answer 11.Var (4X + 3) is (a) 7 (b) 16 Var(X) (c) 19 (d) 0 12.In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is (a) (b) (c) (d)

10 Choose The Correct Answer 13.The mean of a binomial distribution is 5 and its standard deviation is 2. Then the value of n and p is (a) (b) (c) (d) 14.If in a Poisson distribution P(X = 0) = k, then the variance is (a) log(1/k)(b) log k (c) e (d) 1/k

11 Choose The Correct Answer 15.If the mean and standard deviation of a binomial distribution are 12 and 2 respectively. Then the value of its parameter p is (a) ½ (b) 1/3 (c) 2/3 (d) ¼ 16.If a random variable X follows Poisson distribution such that E(X 2 ) = 30 then the variance of the distribution is (a) 6 (b) 5 (c) 30 (d) 25

12 Choose The Correct Answer 17.In 16 throws of a die getting an even number is considered a success. Then the variance of the successes is (a) 4 (b) 6 (c) 2 (d) A box contains 6 red and 4white balls. If 3 balls are drawn at random, the probability of getting 2 white balls is (a) (b) (c) (d)

13 Choose The Correct Answer 19.For a Poisson distribution with parameter = 0.25 the value of the 2 nd moment about the origin is (a) 0.25 (b) (c) (d) If 2 cards are drawn from a well shuffled pack of 52 cards, the probability that they are of the same colours is (a) (b) (c) (d)

14 Choose The Correct Answer 21.In a Poisson distribution if P(X = 2) = P(X = 3) then the value of its parameter is (a) 6 (b) 2 (c) 3(d) 0 22.The distribution function F(X) of a random variable X is (a) a decreasing function (b) an increasing function (c) a constant function (d) increasing first and then decreasing

15 Choose The Correct Answer 23.If f(x) is a p.d.f of a normal distribution with mean µ then is (a) 1 (b) 0.5 (c) 0(d) The random variable X follows normal distribution f(x) = then the value of c is (a) (b) (c) (d)

16 Choose The Correct Answer 25.If f(x) is a p.d.f of a normal variate X and X – N( ,  2 ) then is (a) undefined (b) 1 (c) 0.5(d) – The marks obtained by 400 students in a mathematics test were normally distributed with mean 65. If 120 students got more marks above 85, the number of students securing marks between 45 and 65 is (a) 120(b) 20(c) 80(d) 160

17 Choose The Correct Answer 27.In a distribution of X, the mean and variance are 1.5 and 0.5, then E(X 2 ) is (a) 1.75 (b) 1.5 (c) 2.75(d) The normal probability curve is symmetrical about (a) the x-axis(b) the y-axis (c) the line x = µ(d) the line x = 

18 Choose The Correct Answer 29.In the following probability distribution function the value of ‘a’ is (a) (b) (c) (d) 1 30.If 3 dice are thrown once, the number of elements in the sample space is (a) 6 (b) 36 (c) 216 (d) none X P(X)a2a3a4a5a6a

19 Choose The Correct Answer 31.If X is a continuous random variable then P(a < X < b) = (a) P(a  X  b) (b) P(a < X  b) (c) P(a  X < b) (d) all the three 32.Two dice are rolled and X be the random variable of getting number of ‘3’s. Then P(X = 2) (a) (b) (c) (d)

20 Choose The Correct Answer 33.A continuous random variable X has probability density function f(x) then (a) 0  f(x)  1 (b) f(x)  0 (c) f(x)  1 (d) 0 < f(x) < 1 34.A discrete random variable X has probability mass function p(x) then (a) 0  p(x)  1 (b) p(x)  0 (c) p(x)  1 (d) 0 < p(x) < 1

21 Choose The Correct Answer 35.A continuous random variable X follows the probability law, f (x) = where A =, then the value of k is (a) A (b) 1/A (c) A 2 (d) 0

22 Choose The Correct Answer 36.If the probability law density function of a random variable is given by f (x) =, then the value of k is (a) 2/3 (b) 3/2 (c) 2 (d) 3

23 Choose The Correct Answer 37.F (x) =, –  < x <  is a distribution function of a continuous variable X, then P(x  1) is (a) 3/4 (b)  /4 (c) ½ (d) ¼

24 Choose The Correct Answer 38.If f (x) = is a probability density function of a continuous random variable X, then the value of A is (a) 1 (b) 3 (c) 1/3 (d) log3

25 Choose The Correct Answer 39.The probability density function of a random variable X is f(x) = then the value of k is (a)  /  (b)  (c) 1/  (d)  / 

26 Choose The Correct Answer 40.For the distribution function given by F(x) =, then p.d.f f(x) is (a) (b) x; x > 0 (c) cannot be determined (d) 2x; x<0

27 Choose The Correct Answer 41.A continuous random variable x has the p.d.f defined by f(x) =, then c is (a) 1 (b) a (c) 1/a (d) – a

28 Choose The Correct Answer 42.A random variable X has a probability density function f(x) =, then k is (a) 2  (b) (c) (d) 

29 Choose The Correct Answer 43.The mean of the distribution f(x) = is (a) 1/3 (b) 3 (c) – 1/3 (d) – 3 44.The mean value of p.d.f f(x) = is (a) 0 (b) 24 (c) 1/12 (d) 12

30 Choose The Correct Answer 45.Mean and variance of binomial distribution are (a) nq, npq (b) np,  npq (c) np, np (d) np, npq 46.In a binomial distribution if n = 5, P(X = 3) = 2P(X = 2) then (a) p = 2q (b) 2p = q (c) p = q (d) 3p = 2q

31 Choose The Correct Answer 47.For a Binomial distribution with mean 2 and variance 4/3, p = ? (a) 2/3 (b) 1/3 (c) ¾ (d) 2/  3 48.In a Poisson distribution if P(X = 2) = P(X = 3), then mean = ? (a) 1 (b) 2 (c) 3 (d) 4

32 Choose The Correct Answer 49.Which of the following is or are correct regarding normal distribution curve? (1) Symmetrical about the line X =  mean (2) Mean = median = mode (3) Unimodal (4) Point of inflexion are at X =    (a) 1, 2 only (b) 2, 4 only (c) 1, 2, 3 only (d) all

33 Choose The Correct Answer 50.For a standard normal distribution the mean and variance are (a) ,  2 (b) ,  (c) 0, 1 (d) 1, 1

34 Choose The Correct Answer 51.The p.d.f of the standard normal variance Z is  (z) = (a) (b) (c) (d)

35 Choose The Correct Answer 52.If X is normally distributed with mean 6 and standard deviation 5 and Z is the corresponding normal variate, then P(0  x  8) = (a) P(– 1.2 < z <.04) (b) P(– 0.12 < z < 0.4) (c) P(– 1.2 < z < 0.4) (d) P(– 0.12 < z < 0.04)

36 Choose The Correct Answer 53.The probability density function of the normal distribution is f(x) = –  < x < , then the mean  = (a) 1 (b) 2 (c) – 2 (d) 4

37 Choose The Correct Answer 54.For the p.d.f of the normal distribution function –  < x < , then the mean  = (a) 3 (b) 2/3 (c) 3/2 (d) 6

38 Choose The Correct Answer 55.The p.d.f of the normal distribution is –  < x < , then the variance  2 = (a) ¼ (b) 1/  2 (c) 1 (d) 2

39 Choose The Correct Answer 56.The p.d.f of the normal distribution is –  < x < , then the variance  2 = (a) ½ (b) 2 (c) 3/2 (d) 1/  2

40 Choose The Correct Answer 57.For a normal distribution with mean  = 34 and variance  2 = 16, then P(30 < x < 60) = (where X is normal variate and Z is the corresponding standard normal variate) (a) P(–0.25 < z < 0.25) (b) P(0 < z < 1.625) (c) P(0.25 < z < 1.625) (d) P(–0.25 < z < 1.625)

41 Choose The Correct Answer 58.A random variable X has the following probability mass function, then k is x P(x)k3k5k7k9k11k13k (a) 1/13 (b) 1/36 (c) 1/49 (d) 1/7

42 Choose The Correct Answer 59.A discrete random variable takes (a) only a finite number of values (b) all possible values between certain given limits (c) infinite number of values (d) a finite or uncountable number of values

43 Choose The Correct Answer 60.A continuous random variable takes (a) only a finite number of values (b) all possible values between certain given limits (c) infinite number of values (d) a finite or uncountable number of values

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