Let X have the probability density function given by fx(x) = {e*, 0 < x<∞ 0, otherwise Find the density function of Y

Q: Suppose that X takes values between 0 and 1 and has probability density function x2 (2x +). If Y…

A:

Q: Consider the probability density function 0 if x 1.

A: Given,the probability density function of X isf(x)=0if x&lt;012if 0≤x≤132x4if x&gt;1

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: The exponential probability density function is f(y, 2)= he- for y, 120 Show that the exponential…

A:

Q: Let 0 < x < 1 otherwise 1 f (x) = { be density function of the random variable "X" , then find…

A: In question, Given that X has density function f(x). Then we'll find E(ex). The solution is below,

Q: Let X and Y has joint probability density function AX, Y) = 0<x<2, 0<y<2. 16 Find E( X Y ).

A: Solution: From the given information, the joint probability density function of X and Y is

Q: Let f(x)=k(4x -x²) if 03. (a) For what value of k is f(x) a probability density function? (b) For…

A: Given that  Probability density functions of X  f(x)=k(4x-x2)  , 0&lt;x&lt;3 f(x)=0     , x&lt;0 ,…

Q: f we consider the function f (x) = x2 (with x = position) as a probability density distribution…

A: In this question, concept of Probability Density Function is applied. Probability Density Function…

Q: 2. Let X be a continuous random variable with probability density function (pdf) [3x² 0<x<1…

A: f(x)=3x2.       0&lt;x&lt;1 0.               OtherwiseWe have to find the probability density…

Q: Let X be a positive random variable having the probability density function fx(x) and 1 Y = be a…

A: Solution

Q: (a) Let X defines the length in meter. The probability density function of X is f(x) = x + 1 where a…

A:

Q: *(a) Show that E(X) = aß and V(X) = aß². %3D #(b) Suppose that a = (pdf) of Y | and let Y= (X/ß)?.…

A: Given, Therefore, a.The E(X) and V(X) are given as follows:

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…

Q: 0 <x <1 (cx, f(x)= (0, for other x values a) What must c be for the function to be a probability…

A:

Q: Find the conditional probability density function of Y given X? pte: If the answer is (9+1) write it…

A: Solution

Q: Let f(t) be the probability density function for the time it takes you to drive to school in the…

A: It is given that f(t) is the pdf for the time it takes to drive to school, where t is the number of…

Q: The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation…

A:

Q: Show that the following are the probability density functions: fi(x) = e-*I(0,00)(x) f2(x) =…

A: To prove that f(x) is a pdf, we must show that f(x) &gt;= 0 for all x and, using I[a, b] for the…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!