Presentation on theme: "Discrete Random Variables 3"— Presentation transcript:
1 Discrete Random Variables 3 To be able to calculate the expected value and variance of a discrete random variableTo investigate the effect of multipliers and constants on the expected value and the variance of a discrete random variableTo be able to calculate the expected value and variance of distributions like y=aX+b
2 Expected value and variance formulae E(X) = ΣxP(X=x) = Σxp(x)E(X²) = Σx²p(x)E(Xn) = Σxnp(x)Var(X) = E(X²) – (E(X))²
3 Variance Var(X) = E(X²) – (E(X))² a) x 2 3 4 5 6 7 8 p(x) 1/16 2/16 Example2 four sided die numbered 1,2,3,4 are spun and their faces are added (X).Find the probability distribution of XFind E(M)Find Var(M)a)+12345678x2345678p(x)1/162/163/164/16
5 The random variable X has probability function P(X = x) = kx, x = 1,2, k(x+1) x = 4,5 where k is a constant. (a) Find the value of k (2) (b) Find the exact value of E(X) (2) (c) Show that, to 3 significant figures, Var(X) = (4) (d) Find, to 1 decimal place, Var(4 – 3X) (2) (Total 10 marks)
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