Let EX 5 and EX32 89 Find Var X Find the standard deviatio

Let E(X) = -5; and E[(X-3)^2] = 89. Find Var (X). Find the standard deviation of X. There are 2 defective items in a group of 10. A sample of 8 items is taken randomly from the group. Let the random variable X be the number of defective items in the sample. Construct the probability mass function (pmf) of X. Compute E(X). Compute Var (X) The discrete random variable Y has a Poisson distribution with mean equal to 6. Find the following probabilities.

Solution

1.

a)

E(x) = -5

Also,

E[(X - 3)^2] = 89

Expanding,

E(X^2 - 6X + 9) = 89

E(X^2) - 6E(X) + 9 = 89

E(X^2) - 6(-5) + 9 = 89

E(X^2) + 30 + 9 = 89

E(X^2) + 39 = 89

E(X^2) = 50

Therefore,

var(x) = E(X^2) - E(X)^2 = 50 - (-5)^2 = 25 [ANSWER]

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b)

Thus,

s(x) = sqrt(Var(x)) = 5 [ANSWER]

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