The lifetime in months of a sure component has a gamma distribution with a = B = 2. A enterprise buys 3 such elements and makes use of one till it fails, changing it with a 2d component. When the latter fails, it's far changed with the aid of using the 0.33 component.What are the imply and the variance of the whole lifetime (the sum of the lifetimes of the 3 elements) related to this situation?

38

Let X1,X2,X3 be a random pattern of length three from the distribution with pmf f (x) = 1/four, x = '1, 2, three, four. For example, examine 3 unbiased rolls of a truthful 4-sided die. (a) Find the pmf of Y=. Xi + X2 + X3.

(b) Sketch a bar graph of the pmf of Y.

39

Let X1, X2, X3 be together unbiased random variables with Poisson distributions having manner 2, 1, and four, respectively.

(a) Find the mgf of the sum Y.= X1 + X2 + X3. (b) How is Y distributed? (c) Compute P(three five Y5 nine).

40

Let Z1,Z2, ,Z7 be a random pattern from the usual ordinary distribution N(zero, 1). Let + four. Find P(1.69 < W < 14.07).