What is the distribution of w=x+y+z

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Let X~N(2,6) and Y~N(-3,2) and Z~N(0,1). All three random variables are independent of each other. Do the following.

a. What is the distribution of W=X+Y+Z? What are E(W) and Var(W)?

b. What is the distribution of Q=2Y?

c. What is the distribution of P=-2X+4?

d. Find a and b so that M=a+bX is distributed as a standard Normal Distribution?.

Reference no: EM13832878

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