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3. If a dealers profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the den...
If a dealer's profit, in units of $30003000, on a new automobile can be looked upon as a random variable X having the density function below, find the average profit per automobile. f(x) equals= left brace Start 2 By 2 Matrix 1st Row 1st Column StartFraction 1 Over 22 EndFraction left parenthesis 12 minus x right parenthesis comma 2nd Column 0 less than x less than 2 comma 2nd Row 1st Column 0 comma 2nd Column elsewhere EndMatrix 122(12−x), 0<x<2,...
Assume the life of an electronic component in hours is a random variable with the following density function: 9. f(x)-(01 ge-./soo, elsewhere. Find the following: (a) The mean life of the electronic component, (b) Find E(X2), (c) Find the variance and standard deviation of the random variable X. (d)Demonstrate that Chebyshev's theorem holds for k = 2 and k = 3.
Assume the life of an electronic component in hours is a random variable with the following density function: 9....
4. Let X be a continuous random variable with probability density 1 0< x<3 -x + k =6 f(x) elsewhere 0, Evaluate k. a. b. Find P(1 < X< 2). c. Find E(X) d. Find e. Find ox.
4. Let X be a continuous random variable with probability density 1 0
Let X have probability density function f(2)= k(1+x) -3 for 0 < x < oo and f(x) = 0 elsewhere. a. Find the constant k and Find the c.d.f. of X. b. Find the expected value and the variance of X. Are both well defined? c. Suppose you are required to generate a random variable X with the probability density function f(x). You have available to you a computer program that will generate a random variable U having a U[0,...
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
3 The probability density function of a random variable on the interval [9, 16] is f(x) = x. Find the following values. a. Find the expected value The expected value is (Round to two decimal places as needed.) b. Find the variance. The variance is (Round to two decimal places as needed.) c. Find the standard deviation The standard deviation is (Round to two decimal places as needed.) d. Find the probability that the random variable has a value greater...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
X is a continuous random variable, f(x) is the probability density function (pdf) of X, and F(x) is the cumulative distribution function of X. Then for any two numbers a and b with a < b, which of the following are true? Circle all correct answers. A. B. C. D. 5. If X is a normally distributed random variable with a mean of 36 and a standard deviation of 12, then the probability that X exceeds 36 is: A. .5000...
Assume the length X in minutes of a particular type of telephone conversation is a random variable with probability density function f(x) = {1/5 e^x/5, x > 0 0, elsewhere (a) Determine the mean length E (X) of this type of telephone conversation. (b) Find the variance and standard deviation of X. (c) Find E [(X + 5)^2].
1. [4 points] Consider a random variable X whose probability distribution function is given by 0.4 ifx=0 0.3 if3 0 elsewhere (I) find the value of k (2) find the mean of X (3) find the variance of X