STAT235 Lecture Notes - Standard Deviation, Normal Distribution, Stra

Given independent random variables X and Y with E ( X )=80, σX=10 and E (Y)=85, σY =12 respectively, find the mean and variance of each of the following random variables.

a. W=4X-2Y

b. {X1 ,..., X 100} and {Y1, ...,Y 100} are independent draws from X and Y distributions.

W=y bar -x̅ 

c. {X1,..., X10} are independent draws from X distributions.

W =X1+,...,+X10

d. W=10X

Consider two independent random variables X1 ∼ U(0, 7), X2 ∼ U(0, 1). For the random variables Y = X1 + X2:

• What is the support of the distribution? Is the distribution continuous, discrete or mixed?

• Draw the probability distribution function of the random variable? Justify your answer with either theoretically or logically.

Let y1 and y2 be independent random variables that are both uniformly distributed on the interval (0,1) find P(Y1 < 2*Y2 | Y1 < 3*Y2)