Input all answers to three decimals places and do not input your answers as a percentage.

Alec is taking both a Statistics course and a Geography course this semester. The probability that he passes his Statistics course is 0.65. The probability that he passes his Geography course is 0.92. These two events (passing Statistics and passing Geography) are independent.

1. What is the probability he passes both classes?

2. What is the probability he passes , but fails the other?

3. What is the probability he passes at least

4. What is the probability he passes neither class?

5. What is the probability he passes Statistics and fails Geography?

6. What is the probability he passes Geography and fails Statistics?

JAM 2017 MATHEMATICAL STATISTICS . MS 0.59 Let X1, X2. ...,X100 be i.i.d. random variables with E(X,) = 0, E(X;) = 0?, where o > 0. Let Zie Xi. If an approximate value of P(S 0,1> 0,r >0. If E(X) = 2 and Var(X) = 2, then P(X 80%) in the math course and statistics course?Q:56 Let X1, X2, X3 be independent random variables with the common probability density function f(x) =[ 2e-2x, ifx>0 0 , otherwise Let Y = min {X1.Xz,X3), E(Y) = My and Var(Y) = 03. Then P(Y > Hy + Jy) equals Q.57 Let X and Y be continuous random variables with the joint probability density function f(x, y) = sex, if lyl s x, x>0 otherwise Then E(X | Y = -1) equals Q.58 Let X and Y be discrete random variables with P(Y E {0,1]) = 1, P(X = 0) = = P(X = 1) = 7 W P(Y = 1/X = 1) = 7. P(Y = 0|X = 0) = - Then 3P(Y = 1) - P(Y = 0) equals