3. Suppose X is equally likely to be 0 or 2. (a) What is the mean...
3. Suppose X is equally likely to be 0 or 2. (a) What is the mean of X? (b) What is the variance of X? (c) What is Pr{X-2| X 2)?
The answer mean is 1/3, variance is 1/18 Problem 44.15 Suppose that X has a continuous distribution with pdf. fx (x) = 2x on (0,1) and 0 elsewhere. Suppose that Y is a continuous random variable such that the conditional distribution of Y given X- is uniform on the interval (0, x). Find the mean and variance of Y.
3. Stock A earned -2% last year and 34% this year (each return is equally likely). Stock B earned 6% last year and 2% this year (each return is equally likely). For Stock B: average is 4%, variance is .0004 and standard deviation is 2%. If you put 60% Stock A and 40% in Stock B, find the return and variance of the portfolio.
Additional Problem 5. Suppose that X is equally likely to take any of the values 1, 2, 3, and 4. Let Y sin Ysin㈜ oampate EV). ). Compute E(Y). sin
QUESTION 2: The returns on shares A and B in four equally likely states at the end of next year are summarized below. 30 State Probability Rates of Rates of Return of Return of Share A Share B 0.3 -25 10.4 50 25 0.2 5 -40 0.1 40 30 a. Calculate the expected return, variance and standard deviation for each share. b. Compute the coefficient of correlation for the returns to these shares. c. Calculate the expected return, variance and...
Suppose a point in three-dimensional Cartesian space, (X, Y, Z) , is equally likely to fall anywhere on the surface of the hemisphere defined by X2+y2+2 -1 and Z20. (a) Find the PDF of Z. zz) (b) Find the joint PDF of X and Y. JK.ужд) Suppose a point in three-dimensional Cartesian space, (X, Y, Z) , is equally likely to fall anywhere on the surface of the hemisphere defined by X2+y2+2 -1 and Z20. (a) Find the PDF of...
Suppose the c.d.f. of X is F(t) 3 for 0<t< (a) What is F(5)? (b) What is F(-5)? (c) Compute the p.d.f of X. (d) Compute the mean of X (e) Compute the variance of X. (f) Compute the standard deviation of X (g) Compute the squared coefficient of variation of X.
1. Suppose X has mean 3 and variance 4, Y has mean 5 and variance 9, and Coy(X, Y) =-2. (a) What is the mean of 6X 7Y? (b) What is the variance of 6X TY? (c) What is the variance of 6X - TY? (d) What is the squared coefficient of variation of X? (e) What is the covariance of X and X +Y?
5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider a new random variable, W=2X + 3. i. What is E(W)? ii. What is Var(W)? 6. Suppose the random variables X and Y are jointly distributed. Define a new random variable, W=2X+3Y. i. What is Var(W)? ii. What is Var(W) if X and Y are independent?
Suppose a photon is equally likely to be found anywhere in an interval of 20.5 cm along the x-axis. What is the minimum uncertainty in the photon's x component of momentum