(a) Let X,, N. X be a random sample of size 10 from N(0, o). Find a conslal .... A so that R A(X,-X)/ V has a t-distribution. How many degrees of freedom are associated with the t-distribution? Suppose the mean of the nomal distribution is unknown, explain the effect on R. What changes, if any, would you make on R in order for it to follow a t-distribution? (b) Find P(2y² -32Y +127.968 s0) if Y has a normal distribution with µ-8 and o - 1. (c) Let S' be the variance of a random sample of size 21 from a normal distribution with mea riance 40 Find P6282 < S < 68.34).

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Q: a) compare E(Y|X=x) and E(Y|X) b) Find the pdf of Y c) find the conditional pdf of X given that Y=y

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.