X is a normal Gaussian random variable (fy (x) = g(v) = { {2v v > 0 %3D Find probability density function of Y. Y = a(X)

Q: A random variable X has the probability density function 1 1 f(x) = n x2 + 1' then the probability…

A: Here we've to find, P(1/3<X2<1) We can write it, P(√1/3<X<1)

Q: ariables X and Y are JO two stafistically independent random fx(x) = fu(x – 1)e-x-1)/2 fr(y) = u(y-…

A: Solution

Q: A continuous random variable X that can assume values between x = 0 and x = 4 has a density function…

A:

Q: Random variables X and Y have density functions £x(x) == [u(x)-u(x-a)] a and fy(y) = bu(y)e-by where…

A:

Q: 6) The probability density function of the random variable X whose moment generating function () (1…

A: The moment generating function of X is given by MX(t) = (1/2)(1 + et)

Q: Suppose X~Uniform (0,1), and Y = -ln (1-x). (a). Find the probability density function of Y

A: Given that X follows Uniform distribution with (0, 1). Y=-ln1-X a) Consider, the cumulative…

Q: A random variable X has probability density function given by if z 1 (a) What is the expectation…

A: a) The expectation is calculated as follows: EX=∫01x6x-x2dx=∫016x2-x3dx=6x33-x4401=613-14=612=12

Q: Joint density functions of two random variables is given by fxx (x, y) = 18y² x³ Find (a) E[X], (b)…

A:

Q: (a) Let X be a random variable with PDF ƒ(x) = 1−|x|, |x| ≤ 1. Obtain the MGF of X. (b) Find the PDF…

A:

Q: An electronic product with n identical parts connected in parallel cannot function properly only if…

A:

Q: A random Variable X has a probability Density function. [(π/16) cos(π x/8) 4 ≤ x ≤4 elsewhere fx(x)…

A:

Q: X and Y are two independent random variables with fx (x) = e - u (x) and fy (V) = e. u (y). Find the…

A: Given : fXx = e-x ·uxfYy = e-y ·uyz = x-y

Q: (a) (b) (c) f (x) = c exp (- 6x) x > 0 - cx, -1 0 S(x)=√(²3)*, x = 0,1,2,...

A: The Probability distribution function of continuous or discrete random variable are given then to…

Q: nd the probability density of the sum W = X + Y.

A:

Q: Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 6x2 ; 0 0.8 | X =…

A: (i) To find P(X=0.6, Y=0.6), you need to calculate the probability that both X and Y equal 0.6.…

Q: For two random variables X and Y, the joint density function is Find (a) the correlation fxy(x, y) =…

A:

Q: Consider the random variable X with the uniformdensity having α = 1 and β = 3.(a) Use the result of…

A:

Q: Find the values of constants 'a' and b' such that Fx (x) = [1-a ·e*/b] u (x) is a valid distribution…

A:

Q: QUESTION 2 Two random variables X and Y have the following joint probability density function. f(x,…

A: As mentioned I have done 4th part using the concept of variance.

Q: A random variable X has the density function f(x) = c/(x² + 1), where -<x < 0. (a) Find the value of…

A: a) The total probability is always 1. Using that we get:…

Q: Show that k = O Show that the cumulative distribution function is |y² F(y) = 12 (y² + 2) ) 0 2.…

A: To find the value of k, we will use the fact that ∫-∞∞fydy=1 The cumulative distribution function is…

Q: Let Xa random variable with density function f (x) = e-® . 1(0,00) (2). Determine tha density…

A: # Given: random variable x follow exponential (1) distribution then to find pdf of y=x/(1+x)

Q: 9. (25 points) Let X and Y be a random variables of the continuous type having the joint pdf f(x, y)…

A:

Q: Let (x1, x2, · · · , xn) be i.i.d. samples of a random variable X with probability density function…

A: Given that, the probability density function of X is

Q: Is f(x) a legitimate probability mass function? 1- p)*-1p = p+(1 – p)p + (1 – p)°p +. 1 %3D x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: For an exponential random variable (X) having θ = 4 and pdf given by: f(x) = (1/θ)e^(−x/θ ) where x…

A: We want to find the mean and variance and P(X&gt;3)= ?

Q: Let X and Y be two continuous random variables with joint probability density function: 8 xy ;0<…

A:

Q: OP(X sa) = P (X >a) (ii) P (X > b) = 0.1 %3D

A:

Q: Find the probability density functions of non negative continuous random variables with failure rate…

A: Let X be a non negative continuous random variable.

Q: Find the probability density of the sum W = X+ Y.

A:

Q: The density function of Xis (2(x-1), f(x)= (a) Find the mean E(4X+3); (b) Find the variance σ3x+2.…

A:

Q: The probability density functions of two statistically independent random ariables X and Y are fx(x)…

A: Solution

Q: Let X be a random variable with a probability density function given by £x(x) = {{ 0, Let Y = X². ²,…

A: Here , we have to find the pdf of Y by two different methods. a)     So, we solve the first…

Q: The following is a list of 15 measurements. -16, -39, -6, –-47, 24, -65, –80, 29, 74, 53, 50, 26,…

A:

Q: If X is an exponential random variables with rate 1, then its distribution function is given by…

A: Here it is given that , F(x) = 1 − e−x Let us consider , F(x) = u. Now the distribution function…