Find  P(X=4) if X has a Poisson distribution such that 3P(X=1)=P(X=2)

Q: Find the PSD of a stationary random process for which Auto correlation is RYx (t) 6 e- alt|

A:

Q: An insurance company has a portfolio of car insurance. For a given period of time, it is assumed…

A: Note: Hi there! Thank you for posting the question. As your question has 2 different questions, we…

Q: IEX is a Poisson distribution variable, then its moment generating function is e^(e' -1).

A:

Q: Suppose Y has a uniform pdf over the interval [3,5]. Find its (1) first quartile, its (2) median,…

A:

Q: Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random…

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

Q: Let X be a Poisson random variable with E[X] = ln2. Calculate E[cosπX]

A: Given: Let X be a Poisson random variable with E[X] = ln2. The objective is to calculate E[cosπX].

Q: 5 Let X1 and X2 be independent and identically distributed random variables that follow an…

A:

Q: Suppose a time series Yt is given by a random walk Zt and a white noise process Et where Yt = Zt+Et.…

A: Suppose a time series Yt is given by a random walk Zt and a white noise process Et where Yt = Zt+Et…

Q: Let X be a continuous random variable with PDF 2x 0 < x < 1 fx(x) = {0 otherwise Find the expected…

A:

Q: Develop a random variate generator for a random variable X with the pdf if x < 0, f(x) =- le-2x if x…

A: We have to find the solution for given function.

Q: If X has an F distribution with ν1 and ν2 degrees offreedom, show that Y = 1Xhas an F distribution…

A: Note: Thank you for the question. Since the information is not clear to us, we have considered,…

Q: Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over…

A: Given, The data set is: X Y 1 0 0 1 -1 0 0 -1     To find, The correlation coefficient…

Q: Let X, X, ..., X, be independent random variables from a distribution |(0+1)x° for 0-1 with pdf…

A: # given random variable x with pdf  f(x)=(theta+1)*x^theta  :0&lt;x&lt;1  then to find maximum…

Q: If X, and X, are two independent RVs that follow Poisson distribution with parameters 2, and 2,…

A:

Q: Let X1,..., X,|A be iid Poisson(A), and let A ~ Gamma(a, B), with a, B are known. Give two reasons…

A: Given information: The probability density function of the random variable X is as given below:

Q: Let X be a random variable having a cumulative distribution function F. Show that if EX exists, then…

A:

Q: If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value…

A:

Q: Let X has Poisson distribution with parameter A such that P(X=2) =9P(X=4) +90P(X=6). Find the value…

A: Solution : Given that, Let , X has poisson distribution with parameter λ such that…

Q: Let X1, X2 and X3 be independent and identically distributed random variables that follow a Poisson…

A: Given:- X1 , X2 , X3 , are independent and identically random variables X1 , X2 , X3  ~ Poisson…

Q: Let X, the number of micro-flaws on the surface of a randomly selected, freshly painted car door of…

A:

Q: The CDF of a continuous random variable X is F(x) = 1 - e-/5. Then the pdf of X is

A: We have given that, CDF F(x) = 1 -e-x/5 The pdf is given as f(x)= d/dx( F(x))

Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

A:

Q: The Pareto distribution is frequently used as a model in the study of incomes and has the cumulative…

A:

Q: Suppose X has a uniform distribution on the interval [−2, 3]. Find the moment generating function of…

A: X has a uniform distribution X~U[-2,3]

Q: 3) Let X₁, X₂, X, be mutually independent and identically distributed exponential random variables…

A: Given that  Xi ~ E( β = 1 ) i = 1,2,3,_____,n  X1,X2,____,Xn are independent and identically…

Q: Let x, x2,x, be a random sample of size (n) taken from Poisson( 0), and y = "x, then F(x1, x2, X,…

A: The answer is given using the formula of Poisson distribution.

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

A: Obtain the probability that X greater than equals 2. The probability that X greater than equals 2is…

Q: Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)

A: From the given information,X1, X2, X3 are independent random variable that Exponentially…

Q: X1, ..., Xn be a sample from an Poisson population with parameter λ. (a) Find the maximum likelihood…

A: The probability distribution of Poisson distribution is given by: The maximum likelihood estimator…

Q: The autocorrelation function of a random process Rx (T) cannot have any arbitrary shape.

A:

Q: Suppose X has a uniform distribution on the interval [2,6]. Derive the moment generating function.…

A: Given that X follows uniform distribution on the interval [2,6]. Here, a=2 and b=6 a) Formula for…

Q: The X be a continuous random variable with cumulative distribution function 1 F(x) = 1 for x > 0…

A: From the given information, X be continuous random variable with cumulative distribution is,…

Q: 2a)    The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean…

A: GivenThe number of flowers per square meter in Sarah's garden follow Poisson distribution with mean…

Q: 1. Let X, 2 Poisson(A,), for i = 1,2. (a) Show that X1 + X2~ Poisson(A1 + Ag). (b) Show that X| X +…

A:

Q: Given the random variable x- f(x)=ae for x20. Estimate the moment generating function of x.

A:

Q: 1. Let X, 2 Poisson(A,), for i = 1,2. (a) Show that X1 + Xy~ Poisson(A + A2). (b) Show that X| X + Y…

A:

Q: Let x1, x2X. be a random sample of size (n) taken from Poisson( 8), and y = 2x, then F(x1, x2 , X,…

A: Poisson Distribution: A discrete random variable X is said to follow Poisson distribution with…

Q: 3. If X has a Poisson distribution and if P(X = 0) = 0.25, find P(X > 4). %3D

A: Given : X has a Poisson distribution. P(X=0)= 0.25 PX=x = e-λ×λxx! PX=0 = 0.25 e-λ×λ00!= 0.25…

Q: The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate…

A: Hey there! Thanks for posting the question. Since there are more than three sub-parts in your…

Q: Let random sample of n observations from each of the distributions: a. Poisson distribution with…

A:

Q: For a random variable, its hazard function also referred to as the instantaneous failure rate is…

A:

Q: 3. Suppose that X has a uniform distribution supported on [0, 1]. Find the pdf of Y = – In(X). Does…

A:

Q: Let X1, X2, ..., Xn be a random sample from an exponential population, find the moment estimator for…

A: The mean is calculated as follows: EX= ∫0∞xθe-θxdx      =θ∫0∞xe-θxdx      =θΓ2θ2     =1θ

Q: 2. Show that in a Lorentzian distribution the half width is r.

A: Introduction -   The Lorentizan function is the singly peaked function given by L(x)…

Q: Let X be a random variable with cumulative distribution function 3 x >0 F(x) = x < 0 Determine its…

A:

Q: i) Find the moment generating function of X = -cY. ii) What is the distribution of X?

A:

Q: Find the marginal probability of X = 1.

A: Given:     Y     1 2 3 X 1 0.05 0.05 0 2 0.05 0.1 0.2 3 0.1 0.35 0.1

Q: If the number X of particles emitted during a 1-h period from a radioactive source has a Poisson…

A: