(a) A continuous random variable X is distributed according to a probability den- sity function (pdf) fx(x) = c (1+ x), -1

Q: a. Find the value of the constant c. b. Find E[X] and Var(X) c. Find P [0 < X <-]. с.

A:

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Q: (a) Find the expectation E (X) of X. E (X) = [] (b) Find the variance Var(X) of X. Varlx) = D

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A: Please find the explanation below. Thank you

Q: 3. (a) What is the standard deviation of X? (b) Compute E[X²]. (c) Compute E[X(X - 1)].

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Q.3 A function h(x) is given below. h(x)= (a) Test/check/prove whether h(x) is a valid CDF. (b)…

A: The given function:

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Q: Let X be a continuous random variable with pdf 0 <x <1 1<x < 2 2 < x < 3 ax a f(x) = -ax + 3a…

A: (i) As if f(x) is a pdf then ∫-∞∞f(x)dx = 1⇒ ∫01axdx + ∫12adx + ∫23(-ax + 3a)dx = 1⇒ ax2201 + ax12 +…

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A: Please note that as per our guidelines if multiple questions are posted we can answer the first…

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

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A: Please see the next step for solution.

Q: F(x,y) = { (x+y)/42 ; x = 1,2,3  y = 1,2                 0; elsewhere ] (i) Find the mean for the…

A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

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Q: (b) A continuous p.d.f for a random variable X with function, P(x) = SX for 01|x< 4).

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Q: A random variable X has the pdf as f(x) = ax + b, for 0 < x< 1. The mean of X is E(X) = 2/3. (1)…

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A: The PDF is a probability that a random variable, say X, will take a value exactly equal to x.

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Q: A random variable X has a pdf [c(1-x*) -1<x <1 fx(x) otherwise (i) Find C. (ii) Find P[|x|<1/2].

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Q: Let X be a continuous random variable with pdf f(x) = x² for -1 < x < c. Find the value of c.

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A: Note: Hi there! Thank you for posting the questions. As there are multiple sub parts, according to…

Q: The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp…

A: Thank you posting this question! Since it contains multiple sub-parts, as per the policy, I will…