Suppose X has density function f(x) = cx(1-x) for 0 < x < 1 and 0 otherwise. What value of c should we take to make f a density function? Find P(X < 1/3), E[X], E[X²], Var(X) and E[X"] for n > 2.

Q: Find the proportion X of individuals who can be expected to respond to a certain mail-order…

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 =…

A: The value of c that makes probability density function valid is obtained below: From the given…

Q: Suppose f(x)=3x2, 0<x<1 is a density function of X.  Find P(1/2<X<2).

A: We have given that,  Let x is a random variable having probability density function is,  f(x) =…

Q: )Suppose X is continuously uniformly distributed on [1, 4]. Let Y = ln(X). What is the density…

A: X~Uniform[1,4]

Q: Let f ( x ) = { 0 ,                     i f   x ≤ 0                      c x/ x^ 2 + 1 ,       i f…

A: The provided pdf is,

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

A: Given,f(x)=1-x2     ;  0&lt;x&lt;20             ;  otherwise

Q: The density function of X is given by Sa + br?, 0<I< 1; f(r) = { 0. clsewherce. If o? = var(X) = (a)…

A:

Q: Suppose f(x) = is f(x) a probability density function? if x < 0 , if x ≥ 0 Given that f(x) ≥ 0 for…

A:

Q: For some € (0, 1), define the density on the interval (0, 2) : 0x € (0,1], 0 V (1,2). (a) Verify…

A: Let X be a random variable, a real valued function f(x) will be a probability density function if1)…

Q: A random variable Y has the density function { Se', y<0 otherwise f(y) = Find E(Y ³).

A:

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

A: Since you have asked multiple questions, we will solve first three subparts for you. To get…

Q: Find E(X)

A:

Q: Let Z ∼ N(0,1) and Y = Z1/3 (a) Find the density function (pdf) of Y . b) FindP (Y> (1/4)^1/3))

A: Given:- Let Z ∼ N(0,1)  Y = Z^1/3

Q: Suppose f and g are continuous on [a, b] and f f(x) dx = S% 8(x) dr. Prove that there is cE [a, b]…

A: Suppose f and g are continuous functions on [a, b] such that ∫abf(x) dx=∫abg(x) dx We need to prove…

Q: Problem 8: Consider the density function f(x) = a) Evaluate k. b) Find F(x). c) Use F(x) to evaluate…

A: Given: f(x)=kx4,x&gt;10,x≤1

Q: If X and Y are jointly continuous with joint density function fx,y(z,y), show that X + Y is…

A: Let X and Y are jointly continuous with joint density function fX,Y(x,y) We have to prove that X+Y…

Q: 6. The joint probability density function of X and Y is given by f(x, y) = .0Y). (c) Find P(Y > }|X…

A:

Q: 4. Consider the density function 0.5 <x < 2.5 f(x) = }kvx, 0, %3D elsewhere. a) Evaluate k. b) Find…

A: a) The total area under the probability density function is one.…