Here we are given E(x) =.5 then E(5x+3) =5*E(X) +3
5*.5+3 =5.5the expected value is 5.5
5. Suppose X is a continuous RV modeled by f(x; a) =-e-le-al where-oo < x < 00, If a random sample of size n is drawn with n odd, show the MLE for α is the median of the sample.
Entered Answer Preview – 3x (-3/34) *[e^(-3*x)]*sin(5*x)-(5/34)*[e^(-3*x)]*cos(5*x) gåe-3* sin(5x) – 5 34 e cos(5x) (1 point) Find the integral. |e** sin(5x)dx = (-3/34/E^(-3)sin(52)-(6/34/e^(-3x]cos(52)
Let X be a continuous random variable with density f(x) = e?5x,
x > b. Find b.
A. (ln 5)=5 B. ?(ln 5)=5 C. e?5=5
quad D. 3 E. None of the preceding
Let X be a continuous random variable with density f(x) = e-5x, x > b. Find b. A. (In 5)/5 B. — (In 5)/5 C. e-5/5 quad D. 3 E. none of the preceding
1. Let X be an RV with density f(x) = ¼arosinx + c, x E [-1,11 (f(x) = 0 elsewhere). (a) Compute the constant c. (b) Compute the DF of X. (c) Compute the DF of the RV Y d) Compute P( <0.5) X2.
1. Let X be an RV with density f(x) = ¼arosinx + c, x E [-1,11 (f(x) = 0 elsewhere). (a) Compute the constant c. (b) Compute the DF of X. (c) Compute the DF of...
Problem 1 Let X be a RV with expected value E{X} = 0 and variance Var{x} = 1. In Chebyshev inequality, what integer value k will assure us that P{]X[ > k} = 0.01?
exp(8k- e) ん! 3. Let X be a discrete RV modeled by px(k; B) - for k 0,1,2,.... Here, exp(y) just means e' and is a nice way to show exponents when the expression for y is complicated or has exponentiation in it. If Xi, X2,... , Xn is iid based on X, find the MLE for B
QUESTION 9 Given E(X)=2 and Var(X)=4, let Y =5X-3. Find E(Y) Var(Y)
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C is a curve defined by() ,y int/2),0 st2.
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C is a curve defined by() ,y int/2),0 st2.
For this question, let S be a sample space, and let RV be the set of {0, 1}-valued random variables. Let F : RV → (2^S) be given by F(X) := (X = 1). Let I : (2^S) → RV be the function that outputs the indicator variable for A on input A. Show that I and F are two-sided inverses. Note: 2^S denotes power set of S
Let fx) = 5x- 5 and g(x) = -2x+9. Find: %D %3D (f-3)(3).