For the random variable X, probability density function is given aseª,f (x) = { 0,find the probability distribution of Y =e--0.5(1) e-√y/3□e(¹-√√3/y) √32y³/23e-3x3y3(1+x)²0≤ y ≤30≤ y ≤30≤ y ≤30 ≤ y ≤30 ≤ y ≤3x>0otherwise

Answered: 3 nd the probability distribution of Y…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?
A continuous random variable has the probability density function f(x) = 1/8 for 0 ≤ x ≤ 8. What is the expected value of X?
Suppose that two-dimensional continuous random variable (X, Y) has joint probability density function given by f(x,y) = 24xy, x is less than equal to 1 and greater than equal to 0, y is less than equal to 1 and greater than equal to 0, x+y is less than equal to 1 and greater than equal to 0. Check that E(Y) = E[E(Y|X)] and V(Y) = E[V(Y|X)] + V[E(Y|X)].
The probability density function of the continuous random variable X defined in the set of non-negative real numbers is given as f(x) = 2.exp(-2x). What is the expected value of X?
A random variable X has a Pareto distribution if andonly if its probability density is given by f(x) =⎧⎪⎨⎪⎩αxα+1 for x > 10 elsewhere where α > 0. Show that μ r exists only if r < α.
Let X and Y be independent, uniformly distributed random variables in the range (0 1). If Z = X + Y, what is the probability P[Z < 0.5]? NOTE: The probability density function of a regular random variable defined in the range (0,1) is constant and takes the value 1.
A filling station recieves its supply of gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f(x) = 5*(1-x)4 for 0 less than or equal to x and x less than or equal to 1 and f(x) = 0 otherwise. Find the capacity of its tank so that the probability of its supply being exhausted in a given week is 10%
The random variable X, the particle size (in micrometers) distribution is characterized by the probability density function:f(x) = 3x^(-4) , x > 1 and 0 elsewhereFind the probability that X exceeds 1.8 micrometers?
IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by G(x) = F(x, ∞) for - ∞ <x < ∞ Use this result to find the marginal distribution function of X for the random variable F(x, y) = { (1-e-x^2 ) (1- e-y^2) for x>0, y> 0 and 0 elsewhere
The random variable X, the particle size (in micrometers) distribution is characterized by the probability density function:f(x) = 3x^(-4) , x > 1 and 0 elsewhereFind the probability that X is less than 3.8 micrometers?
Find the probability density functions of non negative continuous random variables with failure rate functions (1) r(x) =x3 , (2) r(x) = 1/(1+x)
The probability density function of a random variable X is given by Find the probability that it will take on a value within two standard deviations of the mean andcompare this probability with the lower bound provided by Chebyshev’s theorem.

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3 nd the probability distribution of Y = (1+)² e- (²) -0.5 □e(¹-√√3/y) 3e-3x 3y y/3 f(x) = { %* 0, 2y³/2 0≤ y ≤3 0≤ y ≤3 0 ≤ y ≤3 0≤ y ≤3 0≤ y ≤3 e-, x>0 otherwise