o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0...
6. Consider a random variable X with pdf given by 0 elsewhere. (a) What is c? Plot the pdf. (b) Plot the cdf of X. Find P(X 0.5< 0.3).
(5 pts) Consider a random variable X with pdf V o S 0.5eX fx(x) = { 0.5e-2 x < 0 x > 0. 0.5 e-> o ΔΙ Let S 4x2 x < 0 g(x) = { 22 x 20, V ΔΙ and let Y = g(X). Determine fy(y).
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 6 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 <X < 0.8)
The random variable X has the following pdf: 2x 0 < x < 1 fx(x) = 0 otherwise Find the s-transform of X, Mx(s) Select one: e-s 1 O a. My(s) = - + S s2 е 1 O b. My(s) = + S 52 52 O c. 1x6) = 2 (6 + 5) O d. 1 My(s) = 2 »=2(+1)
(+3) The pdf f(x) of a random variable X is given by 0, ifx<0 Find the cumulative distribution function F(r
4.3.2 The cumulative distribution func- tion of random variable X is 0 r<-1, Fx (x) = (z + 1)2-1 x < 1, r1 Find the PDF fx(a) of X
If X is a normal random variable with μ =-2 and σ = 3, and has probability density function and cumulative density function fx (z), FX (z), calculate . P(-3< X < 0) F(1/4
Consider the following PDF for a continus random variable f(x) X: 0 x<0,4 Calculate K Calculate P0, 1<x<0,3) Calculate P(X <= 0,2) Calculate E(X) Calculate Var(X) 3,75-Kx®2]
Problem 2 (9 points) Consider a random variable X with pdf given by: (x) 0.06x +0.05 0x <5 4pts P (3.5 < X < 6.5)- Find Find Ex]- 5pts Problem 3 (9 points) Consider a random variable X with pdf given by: f(x) 0.06x +0.05 x -0, 1.5, 2, 4, 5 .ind P(3.5 <X <6.5)- 4pts 5pts Given that EN-3.46, find al