Find the value of C so that the function is a density function. if x < 0 f(x) = {Ce-5² if a ≥ 0.

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A: The solution has been attached below:

Q: a. What value of c will make f(x) a valid density? b. What is P(X = 1)? What about P(X = 1 or X =…

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Q: The density function of X is given by f(x) = 1- x/2, for 0 < x < 2. Find E(5X?). Find Var(X).

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Q: The time to failure in hours of an important piece of electronic equipment used in a manufactured…

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Q: (a) Find k. (b) Find cdf F(X).

A: Here we have given the pdf of continuous Random variable X We have to find the value of K and…

Q: 12x²(1– x) for 0sxs1 f(x) = %3D otherwise

A: Solution

Q: 7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.

A: We have given that f(x,y) = k(1 - x)(1 - y) , for 0 &lt; x , y &lt;1

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Q: (d) What is the median checkout duration ? [solve 0.5 = F()]. (e) Obtain the density function f(x).…

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Q: A continuous random variable X that can assume values between x = 3 and x = 6 has a density function…

A: A continuous random variable X that can assume values between  has a density function given byFor…

Q: . Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant). a. What value of c will…

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A: Given function is f(x)={a+bx2       0≤x≤10                otherwiseE[X]=35

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Q: Is the function defined as follows a density function? fx (x) = 0 for x 4

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Q: c) If we have the following density function: f(x) = cx, 0<x< 2: Find 1. C 2. V(x) 3. F(x)

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A: Given See the handwritten solution

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Q: Let X be a continuous variable with probability density function /(x) cx' defined for 0sxs1, where c…

A: We know that the total probability is always 1.  That means: ∫01f(x)dx=1

Q: Face cards Color Suit Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King Red Hearts AV…

A: We have, Total cards = 52 We have selected 5 cards. Hence, the total number of ways to select 5…

Q: 7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.

A:

Q: 1. Consider the two functions f(x) = C(2x - x³), g(x) = C(2x - x²), 0<x<2. (1) Could f be a…

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Q: Suppose random variable X has a density function f ( x ) = { 2 /x 2 ,               1 ≤ x ≤ 2 0 ,…

A: From the provided information,