## Introduction to Mathematical Statistics |

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Page 17

For each of the following, find the constant c so that f(z) satisfies the conditions of

being a p.d.f. of one random variable X. (a) f(z) = c(3%)*, a = 1, 2, 3, ...,

2, 3, ...

For each of the following, find the constant c so that f(z) satisfies the conditions of

being a p.d.f. of one random variable X. (a) f(z) = c(3%)*, a = 1, 2, 3, ...,

**zero****elsewhere**. (b) f(z) = care-, 0 < x < co,**zero elsewhere**. 1.22. Let f(z) = c/15, a = 1,2, 3, ...

Page 25

(c) f(z) = 1, 2 = 0,

Let f(z) = (9%)*, a = 1, 2, 3, ...,

X. Find the moment-generating function, the mean, and the variance of X. 1.37.

(c) f(z) = 1, 2 = 0,

**zero elsewhere**. d) f(z) = 2/a", 1 < r < co,**zero elsewhere**. 1.36.Let f(z) = (9%)*, a = 1, 2, 3, ...,

**zero elsewhere**, be the p.d.f. of the random variableX. Find the moment-generating function, the mean, and the variance of X. 1.37.

Page 57

Find the probability that exactly four items of a random sample of size 5 from the

distribution having p.d.f. f(z) = (x + 1)/2, — 1 < z < 1,

• 3.26. Let X1, X2, Xs be a random sample of size 3 from a normal distribution ...

Find the probability that exactly four items of a random sample of size 5 from the

distribution having p.d.f. f(z) = (x + 1)/2, — 1 < z < 1,

**zero elsewhere**, exceed zero.• 3.26. Let X1, X2, Xs be a random sample of size 3 from a normal distribution ...

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