Find E(Y), E(Y^2 ), E(Y^3 ), Var(Y)
Find E(Y), E(Y^2 ), E(Y^3 ), Var(Y) Problem 2.6.3 (variation of) The cumulative distribution function of...
3. The cumulative distribution function of a random variable Y is: 0 if y<-1, 0.3 if -1 y <0.5, 0.7 Fr (y)- y < 2, if 0.5 1 if y 2 2. (a) Draw a sketch plot of Fy (y) d) Find the probability mass function, fz(2), of Z -Y2 (e Find El2] and Var(Z) (f) Find El2-321 and Var(2-32). 13 marks]
Problem 3. Suppose that the cumulative distribution function of a random variable X is given by (o if b < 0 | 1/3 ifo<b<1B 2/3 if isb<2 2.9 1 if2 Sb. 3.9 (a) Find P(X S 3/2). (b) Find E(X) and Var(X). 4.10
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...
Let Y be a continuous random variable with the following cumulative distribution function: for y <a 1-e-0.5(y-a)", for y>a where a is a constant. What is the 75th percentile of Y? F(y)= ŞO, Possible Answers [ A ]F(0.75) Ba-v2ln(4/3) ca+ √2ln(4/3) Da-2/in2 Ea+2 Vina
Random variable X has the following cumulative distribution function: 0 x〈1 0.12 1Sx <2 F(x) 0.40 2 x<5 0.79 5 x<9 1x29 a. Find the probability mass function of X. b. Find E[X] c. Find E[1/(2X+3)] d. Find Var[X]
Please answer both. . Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
X is a discrete random variable with cumulative distribution function F(x) as shown in the table below. What is P1[.X<2]? fr F(x) 1/8 30-as 0 100 - 0 m 0 oon 100 0 0 O E. cannot be determined
Consider the cumulative distribution function (cdf)F(y) =0, y≤0,y2,0< y≤1,11≤y. (a) Find E(Y) ifYhas this cdf. (b) Find P(Y >1/3|Y≤2/3) ifYhas this cdf. (c) SupposeY1andY2are a random sample from this distribution. FindP(Y1≤1/2,Y2>1/2).
for the given density table: Y: 1 f(Y) 0.5 0.45 0.05 F(3)-F(2)=? (F is cumulative distribution function) Select one: O 0.4 O 0.05 0 -0.4 o none of these
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.