determine the probability density fucntion of Y = X².

Q: The number X is chosen at random between 0 and 1. determine the density functions of the random…

A: Given information: The number X is chosen at random between 0 and 1.  fx=11-0,…

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: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

Q: Determine the value of c for which the function below will be a probability density functi So(8x' -…

A: Here given thatf(x)=c8x3-x4   ; 0≤x≤80                    ; other

Q: What is the probability density of the area of the circle?

A: Given that  Radius = X, then the area of circle is  A = πX2

Q: Suppose the random variable Y has an exponential distribution with mean 2. Use the method of…

A: The random variable Y has an exponential distribution with mean 2.

Q: If X and Y are random variables and X is a geometric random variable where p = 0.1 then what is

A: Given information: X is a geometric random variable with p=0.1. Y=sinπX Y=

Q: Determine the covariance and correlation for the joint probability density function f(x, y) = ex-y…

A: Given: The given function, fx,y=e-x-y for 0&lt;x and 0&lt;y

Q: fxlx,y) = x2y is a joint probability density function over the range 0<x<2 and 0<y<3 12 Find the…

A:

Q: (a) Let Z = vX. Show that the density function of Z is given by %3| (-). fz(z) = 2a exp z > 0.

A:

Q: Sk(x + 4y) ,0 <x < 2, 0 < y < 1 ,otherwise Let f(x,y) = be the joint probability density of X and Y.

A: From the given information, f(x, y)=k(x+4y), 0&lt;x&lt;2, 0&lt;y&lt;1 The value of k is obtained…

Q: A continuous random variable X has a normal distribution with mean 6. The probability that X takes a…

A: Given information Mean (µ) = 6 P(X &gt; 15) = 0.38 P(Z &gt; z) = 0.38 P(Z &lt; z) = 1 – P(Z&gt;Z) =…

Q: ilometers from home (along the road) is a. What is the probability that you dropped it within 1…

A: Solution

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: Let X1 and X2 be two independent random variables with the following common probability density…

A: E(1Y) = ∫-∞∞1yf(y) dy

Q: X ~ U(0, 15). What is the probability density function?

A: Given that  A distribution is given as X ~ U(0, 15)        X~U(a, b) It is a uniform distribution…

Q: Let X be a random variable with probability density function (PDF) given by, find E(e²) fx(x): = et…

A: Given,PDF of a random variable X is,fX(x)=exx&lt;00otherwise

Q: Let X be exponentially distributed with parameter λ. Calculate the probability density of Y…

A: Let X be exponentially distributed with parameter λ.

Q: If Θ ∼ Uniform(a = 0, b = 3), find the probability density function of sin(Θ).

A: Step 1:Step 2:Step 3:Step 4:The probability distribution of y=sin(θ)f(y):3(1−y2)​1​;0&lt;y&lt;sin(3)

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…