3) Suppose that X₁, X2,...,X₁00 is a random sample from a normally distributed population with mean μ = 25 and variance o² = 36. If Y = 100X₁, S² = 1 Zi=1 100 Y-μY σy Find the mean and variance of Y. b) Find the P(1000 < X <1200). c) State with parameters the probability distribution function of W. 1100 99 (X, Y)², and W =

Q: Let X be a binomial random variable with probability distribution 3-a SOOʻO**, x = 0,1, 2, 3, f(x) =…

A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

Q: 7. Derive the Wigner distribution of the signal s(t) = e+junt

A: we will use the formula of wigner distribution of any signal St  Wx,t=∫-∞∞xt+τ2×x*t-τ2×e-i2πτfdτ…

Q: 7. Calculate the variance of g (X) = 2X + 3, where X is a random variable with probability…

A: The given data is as follows: x0123f(x)

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: Given that 40% of fruit flies of fruit flies posses a certain gene. So, probability that a fruit fly…

Q: 11. The joint probability distribution of the random variables X and Y is f(x, y). Find the…

A: Joint probability density function explain the probability occurrence of two variance. Marginal…

Q: 0. x < 2 1 25x <3 15 3<x < 4 (b) F(x) = 6. %3D 4sx<5 15 , 55x<6 1 , x26 15 2/3

A: We have given that a random variable X has a pdf given by S(x) = (x-1)/k ,   x= 2,3,4,5,6 and k is…

Q: Assume that Xi ’s are independent of each other and independent of N. Further assume that they have…

A:

Q: If "X" is Poisson yandom variable with pavametev u = 3, find the pro babilities for X= 0, 1,2, ?3,4…

A: Given: Poisson parameter = u= 3 to find: probability when x=0,1,2,3,4 or more

Q: 1. If the joint probability distribution of X and Y is given by f(x,y)= **Y for x=0,1,2,3; y=0,1,2,…

A: XY 0 1 2 3 Total 0 0 130 230 330 630 1 130 230 330 430 1030 2 230 330 430 530 1430…

Q: variables X and Y. Using this information answer the questions below. Y=2 4c 2c X=1 X=2 That is, P(X…

A:

Q: 15. Let Y be a r.v. having the geometric distribution with probability function (1-ey-10. y-1,2,3, -…

A: Find  MLE, E(Y) and P(Y≥4)=?

Q: . Given that (x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution…

A: Answer - Given that    joint probability distribution function of x and y                       f(x,…

Q: 6. Two independent random variables X1=(-1,0,1) and X2=(-1.0) can take the following probability…

A: Expected value is also known as mean or average. It used to take average for discrete or continuous…

Q: If X₁, X₂, X3, .., Xn are random sample from a population with mean μ and variance o², then what is…

A: Given that X1,X2,...,Xn is a random sample from a population with mean μ and variance σ2 and…

Q: Show that the mean and variance of the random variable Y are 0 and 1, respectively.

A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1,

Q: epartment in a small town has a Poisson distribution with mean mu = 10 visits per week. Use Table…

A: (Please not since the mentioned table is not provided we have used the MS-Excel to calculate the…

Q: II. Let X be a discrete random variable with possible values xi, i=1,2,..., and p(xi)=P(X=xi) is…

A: The given statements can be completed as follows, Let X be a discrete random variable with possible…

Q: 3.5 Determine the value c so that each of the follow- ing functions can serve as a probability…

A: We have given that the probability distribution of discrete random variable X. In discrete…

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: 40% of the fruit flies posses certain gene. So, probability that a fruit fly posses that gene = 0.4…

Q: 6. The distribution function of a continuous random variable X is given by F(x)=1-(1+x)e*, x ≥ 0.…

A:

Q: 2. Let X be a random variable with the Poisson distribution, parameter 2. Show that, for w = 1, 2,…

A: X~Poisson(λ) Therefore P(X=x)=e-λλxx! ; x=0,1,2,……

Q: 12. Suppose that X is a random variable for which the m.g.f. is as follows: V(1) = (4 + e' +e) for…

A: The random variable X has a moment generating function ψ(t)=164+et+e-t        for -∞&lt;t&lt;∞ We…

Q: 2. Show how the Poisson distribution -m m e (x= 0, 1, 2,...) %3D х! can be regarded as the limiting…

A:

Q: Question 2 et Y~ B(n = 2,p=0.5). 1. Construct the probability distribution table for Y. k P(Y = k) =…

A: Given that  Y~binomial (n,p) n=2 , p=0.5

Q: Question 4. The random variables X and Y have the joint pdf given by fxy(r, y) = e*, I> 0, 0 < y <…

A: We have given that  The random variables X and Y have the joint pdf given by fXY(x, y) = e-x.…

Q: 4.2 The probability distribution of the discrete ran- dom variable X is 3-a f(x) = , r = 0, 1, 2, 3.…

A: Given : , x = 0,1,2,3

Q: 5. and Y is The joint probability distribution function of two discrete random variable |x -y| 15…

A:

Q: 7. Suppose that X is a random variable for which the m.g.f. is as follows: V(1) = -(3e' + e!) for -0…

A: The moment generating function of the random variable X is given as, MX(t)=E(etx)=ψ(t) =143et+e-t…

Q: 2. Consider the probability distribution on the next slide and prove that:. a. E (; x) = ¿E(X) b. V…

A: Joint Probability Distribution: Let X and Y be two discreate random variables defined over the…

Q: Suppose two independent discrete random variables X₁ and X2. Both follow a discrete distribution…

A: It is given that: PX1=1=PX2=1=p1=0.5PX1=2=PX2=2=p2=0.3PX1=3=PX2=3=p3=0.2 The variables X1 and X2 are…

Q: Consider the following probability distribution where random variable X denotes the number of cups…

A: Given data is  x 0 1 2 3 4 5 P(x) 0.35 0.40 0.16   0.02 0.02

Q: Telephone calls enter a college switchboard on the average of two every three mimutes. The…

A: According to guidelines we solve first question when given questions are different.

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: Let X be a Poisson random variable with parameter λ. Show that the probability that X is even is…

A: Given that, X be a Poisson random variable with parameterλ. We need to show that the probability…

Q: 1. If the joint probability distribution of X and Yis given by f(x, y) x+y for x = 0,2,3; y = 0,1,2…

A: Given : The joint probability distribution function isf(x,y)=x+y30

Q: 3. Consider a Exponential Distribution with parameter of 0.0025 i.e. Exp(0.0025) B. Compute the…

A: Given  X~exp(parameter=0.0025)