Question 3 Suppose fy(y) = 5.e-1/18 for y 20. Calculate PlY>3) 1.649 .6065 O 1 0.0674
Suppose FY (y) = y3 for 0 ≤ y < 1/2, and FY (y) = 1 − (1-y)3 for 1/2 ≤ y ≤ 1. Compute each of the following. (a) P(1/3 < Y < 3/4) (b) P(Y = 1/3) (c) P(Y = 1/2)
6. (5 marks) Suppose Y is a Normal random variable. If P(Y <1)=0.25 and P(Y > 0)=0.9. what are y, and o?
3. Suppose that X has pdf fx(x) = 3, x > 1 and Y has pdf 24» fy(y) = ¡2, x 〉 1. Suppose further that X and Y are inde- pendent. Calculate the P(X 〈 Y).
Problem 2: 20 points 10 5 + 5) A continuous random variable (Y) has a density, fY (3e-3V for y>0 and f () 0, elsewhere. Given Y y, a discrete random variable, N, is Poisson distributed with the rate equal to y TA 1. Derive the marginal distribution of N 2. Determine the marginal expectation of N, EIN 3. Determine the marginal variance of N, Var[N]
Need help with question 2 (not question
1)
1. Suppose that (X,Y) is uniformly distributed over the region {(x, y): 0 < \y< x < 1}. Find: a) the joint density of (X, Y); b) the marginal densities fx(x) and fy(y). c) Are X and Y independent? d) Find E(X) and E(Y). 2. Repeat Exercise 1 for (X,Y) with uniform distribution over {(x, y): 0 < \x]+\y< 1}.
Question 5 of 18 > The decomposition of N, O, can be described by the equation t(s) 0 165 406 795 [N,O31(M) 1.881 1.696 1.457 1.141 2N, O,(soln) -4NO, (soln) + 0, (g) Consider the data in the table for the reaction at 45 °C in carbon tetrachloride solution. Given the data, calculate the average rate of reaction for each successive time interval. What is the average rate of reaction for the time interval from 0 to 165 s? average...
can you solve 1 and 2 please???
1. Calculate E(Y) and SD(Y) for the random variable Y with pdf gy (y) = -7?, 1<y<4. 2. The random variable X has mean jix = 12 and standard deviation o x = 5. Define a new random variable Y = ax + b. (a) Calculate My and oy when a = -2 and 6 -3. (b) Calculate the values of a and b that result in My = 20 and a 100.
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
QUESTION 3 Find the limit. lim (x,y)-> (1, 2) * In y O In (2) - 1 In 2 o 2 No limit
Question 27 Graph the solution set of the system. y2r? y<x+3 o 5+ 4 1 1 4 5 T2 1+ A++ -54 2 1 2 3 15 -1 -2+ =3 HE+ - + O S 4 3 2+ 1+ -54 + 5 Re 2 2 4 * ů o . 3 s 3 2 3 4 ET? T None of these