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I have part a answered but I am lost on how to answer part b. 5. Le.pdf

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I have part a answered but I am lost on how to answer part b. 5. Let X1,X2,,Xn be independent random variables with means 1,2,,n and variances 12,22,,n2, respectively. (a) Show that Y=a1X1+a2X2++anXn has mean Y=a11+a22++ann and variance Y2=a1212+a2222++an2n2 blems 141 (b) Show that if X1,X2,,Xn in (a) have normal distribution, then Y also has a normal distribution with mean Y and variance V2..

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I have part a answered but I am lost on how to answer part b. 5. Let X1,X2,,Xn be independent random variables with means 1,2,,n and variances 12,22,,n2, respectively. (a) Show that Y=a1X1+a2X2++anXn has mean Y=a11+a22++ann and variance Y2=a1212+a2222++an2n2 blems 141 (b) Show that if X1,X2,,Xn in (a) have normal distribution, then Y also has a normal distribution with mean Y and variance V2.

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