Question  #### Earn Coins

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions
• ### 1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1"... 1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1" with ? > 0, ? > 0, constants x > ?, (a) 5 points Find the value of constant c that makes f(x) a valid probability mass function. (b) 5 points Find the cumulative distribution function (CDF) of X.

• ### 2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given... 2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)

• ### 4. (30pts) A continuous random variable X has the probability density function: hx - 1 sx... 4. (30pts) A continuous random variable X has the probability density function: hx - 1 sx 32 f(x) =Jo-hx 2 x 3 0 x >3 which ean bo graphed as f(x) 1 2 a) Find h which makes f(x) a valid probability density function b) Find the expected value E(X) of the probability density function f(x) c) Find the cumulative distribution function F(x). Show all you work

• ### PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks... PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...

• ### Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is... Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.

• ### Suppose that a random variable X has a (probability) density function given by 52e-2, for x... Suppose that a random variable X has a (probability) density function given by 52e-2, for x > 0; f(x) = 0, otherwise, (i) Calculate the moment generating function of X. [6 marks] (ii) Calculate E(X) and E(X²). [6 marks] (iii) Calculate E(ex/2), E(ex) and E(C3x), if they exist. [3 marks] (iv) Based on an independent random sample X = {X1, X2, ..., Xn} from the dis- tribution of X, provide a consistent estimator for 0 = E(esin(\)), where sin() is...

• ### Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed... Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...

• ### 7. The random variables X and Y have joint probability density function f given by 1... 7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.

• ### 7. The random variables X and Y have joint probability density function f given by 1... 7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.

• ### For a continuous random variable X with the following probability density function (PDF): fX(x) = (...

For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)