In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Poisson distribution with probability mass function f(x), where f(x) = θ x e −θ/x! and θ is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats,

Q: 3. Given that the continuous random variable X has distribution function Fl2) as F(x) =0 when 2<1…

A: The graph is given below: From The graph it is concluded that when x approaches 1 from both the…

Q: d. calculate Var (X)

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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: B. Let X and Y be random variables and let A e B. Prove that the function

A: SOLUTION ;

Q: Let Y,, Y2, ..,Y, denote a random sample from a power family distribution with parameter 0. (8y9-1…

A: Given information: fy=θyθ-13θ, 0≤y≤3 2.1 Consider, Ey=∫03yfydy         =∫03y*θyθ-13θdy…

Q: If for a poisson variate 2p ( x = 0 ) = p ( x = 2 ). Find the probability that %3D i) p(x<3), i)…

A: It is given that 2Px=0=Px=2. The pmf of a Poisson distribution is PX=x=e-μμxx!.

Q: b) Two PINS are chosen independently and at random, and you are given that each consists of four…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given that the discrete random variables X has probability mass function, Pr(X=x)= (x/6 where…

A: The probability distribution table is  x p(X) cf 1 0.166667 0.166667 2 0.333333 0.5 3 0.50…

Q: Suppose X and Y are independent random variables, each of zero mean. Assuming that the respective…

A: We have given that the two random variables X and Y are independent and each of zero mean.

Q: 10. Let X, Y be random variables. Suppose thatA IS exponentially distribi 1. Given X = 1, Y is…

A: As X~ Exp(1) and Y/X=x ~ U(x, x+2) Answer : E(Y) = 2

Q: To compare the effect of hospital prenatal nutritional counseling on newborn birthweights, we…

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

Q: If x is approximately  Poisson, compute ( P(X=2), Px=10, pX=0, pX=0.5. If the mean = 3

A:

Q: A circle of radius r has area A = r. If a random circle h

A: Given, a circle of radius r has the area A=πr2.  If a random circle has a radius that is uniformly…

Q: 4. If X~ N3 (μ, E) where µ¹ = [2-3 1] and Σ = 1 3 2 | 1 2 2 then find the distribution of 3X1-2X2 +…

A:

Q: Suppose Y is a Poisson random variable with rate A. Let X be a random variadie be such that given Y,…

A: It is given that the Y~ Poisson(λ) and X|Y=y ~ Gamma(1,Y) We have to find that the E(X) and Var(X)

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: 7. The probability mass function (PMF) is expressed as PMF = P(X = k) = - k(k +1) म्कग ,k =1,2,..,0…

A:

Q: 3. In a Binomial distribution if n= number of trials =8, given that 4P(x=5) =P(x3=3). Find the value…

A: Note: Hey, since there are multiple questions posted, we will answer one question. If you want any…

Q: i. ii. iii. the value of k; the cumulative distribution function of X; P(X <3). P(X<3).

A: Given that  Probability mass function of X is  P(X = x) = kx2  , for x = 1 , 2 , 3 , 4

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: If Z is a discrete random variable with possible values of -1, 0, and 1, and the probability mass…

A: The standard deviation of Z is calculated as follows:

Q: 3. Let X be a discrete random variable whose probability mass function p(x) given as follows. Show…

A: P(X = 1: 5) = ? ===============

Q: Let X1, X2, X3 form a random sample from U(0,1). Find a- The distribution of the second order…

A:

Q: Example 5-17. The elementary probability law of a continilolS f(x) = yoe-), asxS0, b>0, where a, b…

A:

Q: we are given independent random variables X and Y distrubuted:  X ∼ poisson(θ) , Y ∼ poisson(2θ),…

A:

Q: A. P(X¯>1039) B. P(X¯844)

A: From the provided information,    Mean of normal distribution µ=900 Standard deviation is σ=220 And…

Q: 1. The probability distribution function of the maximum annual wind speed v is given by: [-] with…

A:

Q: is 0 otherwise. Find the conditional probability that Yis 2 given X is 3.

A: Given that, The joint probability distribution function of X and Y is, f(x,y) = xy18,   for the…

Q: If Xhas the Poisson distribution with P(X=1) = 2P(X=2), then P(X ≥ 2) is approximately

A: The probability mass function for Poisson random variable X is, Given that P(X=1)=2P(X=2).

Q: Consider the formula: P(x) = x2/21, x = 0, 1, 2, 4. Is P(x) a probability mass function? If so, show…

A: Solution: 9. From the given information,

Q: from a population given by 1 for x> 8 g(x; 0,8) = elsewhere ind estimators for 8 and 0 by the method…

A: Solution

Q: Suppose 1.8% of every Filipino births result in twins. From a random sample of 1000 births, let X be…

A: Answer:- Given, 1.8% of every Filipino births result in twins . Let , p = 1.8% = 0.018  Random…

Q: Hom variable X has the gamma p. d. f with integer j rary ß>0, then E(Xk) is

A:

Q: 4. Probability maximization: We have independent random variables X and Y with distribution X ~…

A: This question seeks to calculate the probability maximization estimator (ϕ^) for two independent…

Q: Given that a random variable X have a Poisson distribution with 2; Find E[cos(nX)] if E(X) = In 2

A: Given information: X = a Poisson random variable The expected value of X is: EX=ln 2=λ It is…

Q: 1. What is the probability that an arrival to an infinite capacity 4 server Poison queueing system…

A: Given information: λμ=3P0=110c=4