SOLUTION REQUIRED WITH COMPLETE STEPS A continuous random variable X has pdf ?x(?) = (? +...

SOLUTION REQUIRED WITH COMPLETE STEPS

A continuous random variable X has pdf ?x(?) = (? + 1) ? ² , 0 ≤ ? ≤ ? + 1, Where B=7.

a) Find the value of a

b) Find cumulative distribution function (CDF) of X i.e. ?x(?).

c) Find the mean of X

d) Find variance of X.

Expert Solution

thank you.

orchestra answered 1 year ago

(15 pts) Suppose that the continuous random variable X has pdf ?(?) = { ?; 0...

(15 pts) Suppose that the continuous random variable X has pdf ?(?) = { ?; 0 < ? < 2 2?; 5 < ? < 10 0; otherwise a) Determine the value of c that makes this a legitimate pdf. b) Sketch a graph of this pdf. c) Determine the cumulative distribution function (cdf) of X. d) Sketch a graph of this cdf. e) Calculate ? = ?(?) and ? = ??(?). f) What is ?(? = ?)? g) Compute...

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤...

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤ x ≤ 2 (a) What should a be in order for this to be a legitimate p.d.f? (b) What is the distribution function (c.d.f.) for X? (c) What is Pr(0 ≤ X < 1)? Pr(X > 0.5)? Pr(X > 3)? (d) What is the 90th percentile value of this distribution? (Note: If you do this problem correctly, you will end up with a cubic...

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 <...

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 < x < 1, 0 elsewhere. (a) Find the value of c such that fX(x) is indeed a PDF. (b) Find P(−0.5 < X < 0.3). (c) Find the median of X.

SOLUTION REQUIRED WITH COMPLETE STEPS Let X be sum of 25 iid random variables, each random...

SOLUTION REQUIRED WITH COMPLETE STEPS Let X be sum of 25 iid random variables, each random variable has mean 60 and standard deviation 20. a) Estimate probability of ? ≥ 1700. b) Estimate probability of 1300 ≤ ? ≤ 1700

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf...

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf is given as Px,y = ?(? + ? + 2)/(B + 2) for 0 ≤ X < 3, 0 ≤ Y < 3 (Where B=0) a) Find the value of ? b) Find the marginal pmf of ? and ? c) Find conditional pmf of ? given ? = 2

A continuous probability density function (PDF) f ( X ) describes the distribution of continuous random...

A continuous probability density function (PDF) f ( X ) describes the distribution of continuous random variable X . Explain in words, and words only, this property: P ( x a < X < x b ) = P ( x a ≤ X ≤ x b )

2] Let x be a continuous random variable that has a normal distribution with μ =...

2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 . Round your answer to four decimal places.

Let x be a continuous random variable that has a normal distribution with μ = 60...

Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n ≤ 0.05N, where n = sample size and N = population size, find the probability that the sample mean, x¯, for a random sample of 24 taken from this population will be between 54.91 and 61.79. Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n...

Suppose that T (≥ 0) is a continuous random variable. Let its pdf, cdf, survival function,...

Suppose that T (≥ 0) is a continuous random variable. Let its pdf, cdf, survival function, hazard rate function, and cumulative hazard rate function be f(t), F(t), s(t), h(t), and H(t), respectively. Note that H(t) is defined by R t 0 h(u)du. a. Denote s(t), h(t), and H(t) as a function of f(t). b. Denote f(t), h(t), and H(t) as a function of s(t). c. Denote f(t), s(t), and H(t) as a function of h(t). d. Denote f(t) and s(t)...

Suppose that a random variable X has a pdf f(x) = ke^(-3x^2+6x-5), -infinity < x <...

Suppose that a random variable X has a pdf f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity (a) Find k. (b) Find the mean and variance of X. (c) Find the probability that X is between 1 and 1.5.

Question