Problem 1) The cumulative distribution function of the continuous random variable X is: 0. x < -1 Fx(x)=(r+1, -1< x<1 %3D x 2 1 a) Find P(X> ½). b) Find P(-5/4

Q: 2.5.8) Suppose that Y is a continuous random variable whose pdf is given by f(x) = {K (4y = 2…

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Q: 1. Let X1, Xn be i.i.d. random variables with a pdf .... f(x) = = e-(x-0), 10, x > 0, elsewhere for…

A: The objective of the question is to compute the cumulative distribution function (CDF) of Y and Zn,…

Q: a. Find the probability that an ordinary coin was selected, given that heads was the result of the…

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Q: Suppose that a pdf for a continuous random variable Y takes the form ayya-1 (1 + yª)r+1 y > 0 f() =…

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Q: 1. Suppose that the random variable X has the pdf given by T(a+B) pa-1(1 – x)ª-1 Г() f(x) = for 0 <…

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Q: If xy Xy .... Xy is a random sample from the distribution. f (x, 0) er (1- 0)-x, x = 0, 1 and 0< 0<1…

A: Answer: For the given data,

Q: (34) Let X be a random variable with p.d.f. 1<x<» k f(x) = { find k. O.w

A: Formula used: fx=x-2k           1&lt;x&lt;∞0                   Otherwise

Q: 2. A random variable X has pdf |x| < 1 elsewhere. cx(1+ x) a. Find c. b. Find E{X}and V AR{X} c.…

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Q: Let x be a random variable Gaussian with zero mean and variance 1. Find: a)The conditional pdf and…

A: To find the mean and Variance of positive half normal distribution

Q: Determine the probability that exactly three of the balls are blue

A: Total bumber of balls = 12 Number of blue balls = 7 Number of red balls = 5 Sample size = 4

Q: If X is a binomially distributed radom variable with E(X) var (X) 4/3; find the distribution of X. 2…

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Q: 9) The initial cost of a random investment is negotiable. The lifetime is 5 years. The MARR is 10% a…

A: According to the above statement

Q: 7. Let X and Y be two independent exponential random variables with pdf's fx(x) = (-) e-x/2 x>0 And…

A: Given X~exp(1/λ) and Y ~exp(1/λ) X and Y are independent

Q: If E(X) = 6 and E[(X) (X-1) ] = 51, find the second moment= 1 and the variance of X= 2

A: Given Data: E(X)=6 E[(X) (X-1)]=51

Q: A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x-x²+4) =

A: Given that E(X) = 1.5, and var(X) = 0.25 The var(X) is defined as Var(X) = E(X2) - (E(X))2

Q: 1 The continuous random variable X has p.d.f. f(x) where f(x) = ¿x for 0<x<4 = 0 otherwise.

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Q: If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?

A: The probability density function of Xf(x)=2x/k2      for 0&lt;x&lt;kfor what value of k the…

Q: (i) If X is a Poisson variable such that P(X=2) = 9P(X=6). Find the mean variance of X (ii) A…

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Q: 20. A continuous random variable X has CDF given by if x <1 F(x) ={2(x – 2 + 1/x) if 1<x<2 if 2 < x…

A: As Prof. A. K. Giri defined, "Probability Density Function: A continuous function f(x) is said to be…

Q: Problem 2 Consider a random variable with cdf(x) = 1-exp(-10x) when x2 0. And 0 otherwise. a)…

A: Given that  Cumulative distribution function of X is  F(X=x)=1-e-10x  , x ≥ 0          = 0    ,…

Q: uppose X and Y are independent random variables. If the pdf of x is xe ",x ≥ 0 and the pdf of y is…

A: Solution

Q: 2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution…

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Q: Consider the continuous random variable X whose pdf is given by f(2)=√15.50(2). (a) Find the value…

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

Q: 4. If the random variable X has an show that for a > 0, b>0, exponential distrib f(x) = x/4, for x ≥…

A: For the random variable X~Exponential1λ, it is given that: fx=1λe-xλ, for x≥0

Q: A continuous random variable has p.d.f. f(x) where { kx 0-x -1 f(x) - k(2-x) 1-x =2 otherwise Find…

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Q: 13. Find the MGF of a random variable whose moments are u, = (r +1)! 2". Ans Mx(t) = (1-2r) 14. If a…

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Q: If a random variable X has pdf ?(?) = 3/376x(1−?), 0 < ?< 1 and

A: Given pdf of X is, f(x)=3376x(1-x), 0&lt;x&lt;1 Given  y=x+1y2=x+1y2-1=x2y=dxdy Limits for Y: If…

Q: 16 a) A random variable has pdf £x (x) = ² (1-x²) fx 4 0 (1-x²) 0≤x≤1 Find E (4x+2) and E(x²). else…

A: Given information: f(x)=541-x4      ; 0≤x≤10                     ; Elsewhere

Q: If random variable x is exponentially-distributed with mean a= 2, calculate p(X> 3)· Σ 2e-2x x=3 E…

A: From the provided information, Mean (λ) = 2 X~exp(2)

Q: Question 7. 7(a). Let Xn be the sample mean of the random sample X₁, Xn from a Poisson distribution…

A: Given Information: X1,X2,....,Xn is a sequence of n random variables. X¯n is the sample mean of  the…

Q: Suppose that X,, X2,...,X, denotes a random sample from a Poison distribution with mean 2. Find the…

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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: Example 11: Find the maximum likelihood estimator for p when f (x ; p) = p* (1 - p)'-× for x 0, 1.

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Q: PROBLEMS 2.1 Apply the inverse-transform method to generate a random variable from the discrete…

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Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

A: Random Variable: A random variable is a real valued function that assign a real number to each…

Q: Consider the continuous random variable X whose pdf is given by f(z)=(a-³) LOSISI(I). (a) Find the…

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

Q: 1) Determine the value of c. 2) Find (a) P{|x| < 1}, (b) P{X² < 9}, and (c) P{X = 1}

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