Consider the random variable X with PDF f(x)=Ke^{-3x} for 0<x<infinity
a. Write value of K so f is PDF
b. Write the expected value
c. First Quartile
Consider the random variable X with PDF f(x)=Ke-3x for 0<x<infinity a. Write value of K so...
3. Let X be a continuous random variable with the following PDF f(x) = ( ke 2 x 20 f(x)= otherwise where k is a positive constant. (a). Find the value of k. (b). Find the 90th percentile of X.
Let the random variable X have the pdf f(x) = e^(-x) for 0 < x < 1, and 0 elsewhere. Compute the probability that the random interval (X; 3X) includes the point x = 3. What is the expected value of the length of the interval?
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
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]
L.9) Hand calculation of expected values a) The pdf of a random variable X with the Exponential[u] distribution is for 0x Calculate by hand the expected value of X b) The pdf of a random variable X with the Beta[2, 3] distribution is 12 ( 1-xf x for。S$ 1. Calculate by hand the expected value of X. c) Go with numbers a and b with a<b. Calculate by hand the expected value and variance of a random variable uniformly distributed...
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
2. Suppose that the continuous random variable X has the pdf f(x) = cx3:0 < x < 2 (a) Find the value of the constant c so that this is a valid pdf. (10 pts) (b) Find P(X -1.5) (5 pts) (c) Find the edf of X use the c that you found in (a). (Hint: it should include three parts: x x < 2, and:2 2) (20 pts) 0,0 <
Consider an exponentially distributed random variable X with pdf f(x) = 2e−2x for x ≥ 0. Let Y = √X. a. Find the cdf for Y. b. Find the pdf for Y. c. Find E[Y]. If you want to skip a difficult integration by parts, make a substitution and look for a Gamma pdf. d. This Y is actually a commonly used continuous distribution. Can you name it and identify its parameters? e. Suppose that X is exponentially distributed with...
o 3.4 For a random variable for which the PDF is (0, x<-1 x> 1 Determine (a) A, (b) μ, (c) o", (d) sh, (e) ku. 3.5 Suppose that (a) Find f(x). (b) Determine,e and o". (c) Find the expected value of e.
E. Consider a continuous random variable X with cdf F(x) = x3/8, 0 < x < 2. (27) The pdf f(x) of X is (а) 6х (b) x3/8 (c) 3x2/8 (d) x2/4(28) E[X2+3X] is (а) 6.9 (b) 4.3 (с) 4.5 (d) 8.1 (29) The probability P(X > 1) is (a) 7/8 (b) 4/8 (c) 6/8 (d) 3/8