# mathematics

QUESTION 1
The discrete random variable X has the following probability distribution function.
x 0 1 2 3 4
P(X=x) 0.3 0.2 0.1 0.3 0.1

Find
(a) The expected value of X, E(X)
(b) The variance of X, Var(X)
(c) The standard deviation of X, σ
(d) E(2X)
(e) Var(2X)

QUESTION 2
The probability distribution function of a discrete random variable X is
f(x)={(x^2/55 ,x=1,2,3,4,5)/(0 ,otherwise)}
(a) E(X)
(b) Var(X)
(c) E(3X+2)
(d) Var(3X+2)
(e) 5E(2X-1)
(f) E(2X+1)^2

QUESTION 3
The probability distribution function of a discrete random variable X is given below
x 1 2 3 4 5
P(X=x) 0.3 c 0.1 3c 2c
(a) Find the value of c.
(b) Var(X)

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