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

Q: Suppose that the random variable X has a lognormal distribution with parameters - = 0 and w? = 4.…

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Q: If X is a Poisson variable such that P(X= 2) = 9P(X = 4) + 90P(X=6), find the mean and variance of…

A: Let X be the random variable from Poisson distribution  with P(X=2) = 9P(X=4) + 90P(X=6)  Then,  We…

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: f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the…

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Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X.

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Q: The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular…

A: (As per the bartleby guidelines, for more than one question asked, only first one is to be solved.…

Q: Let X1, X2,...Xn be a random sample from a Poisson distribution with variance 0. Find an unbiased…

A: Let, X1, X2…Xn be a random sample from Poisson distribution with variance = θ For Poisson…

Q: If the variance of a continuous random variable X with pdf f(x) is noted as V(X), what is its…

A: Given: X had pdf f(x) and Variance of random variable X is - V(X)

Q: If Y is an exponential random variable with parameter , then μ = E(Y) = 8 and o² = V(Y) = 8². The…

A: We have given that Y is an exponential random variable with parameters beta then mean = E(Y) = β…

Q: If X is a random variable having a normal distribution with the mean μ and standard deviation σ, how…

A: Let X be a continuous random variable having a normal distribution with the mean μμ and standard…

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

A: (a) The probability distribution function for the exponential distribution with parameter λ is given…

Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

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Q: What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?

A: The parameter of the Poisson random variable is l.

Q: If a random variable X has the moment generating function Mx (t) = 2 - ť Datermine the variance of…

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Q: X and Y be standard normal random variables with correlation p. Compute the joint and marginal…

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Q: Suppose you fit a simple Poisson model such that In A = XB where B = 1.9. What would the variance be…

A: Given data

Q: Suppose X is a random variable of a normal distribution with E(X)=2 and Var(X)=4. Find P(X<4)

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is…

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Q: If has a Poisson distribution such that P(X 21)=0.8646 then then the variance of is equal to

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Q: A random variable has poisson distribution such that P (X =3) = P (X= 4). Find P (6).

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Q: Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

A: The geometric distribution and Poisson distribution are two different types of probability…

Q: Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)

A: A uniform distribution is a probability distribution that has constant probability. So, it is also…

Q: Our random variable X has a beta distribution with a = 7 and B = 3. What is the mean of X? E(X) =

A: GivenA random variable X follows beta distributionwith α=7 and β=3

Q: In a poisson distribution P(X=0)=P(X=2).Find the variance V(X) of X.

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Q: In the daily production of a certain kind of rope, the number of defects per foot given by Y is…

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Q: Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random…

A: Given,F(X)=1-e-x3   ;  x≥0

Q: The Poisson distribution gives the probability for the number of occurrences for a "rare" event.…

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

A: Here in this question given that, the number X of particles emitted during a 1 hour period from a…

Q: pose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square…

A: It is given that Y has an exponential distribution with mean Beta, i.e. Y∼Exp(1/β) since for…

Q: If pdf of a random variable is given by fx(x) = e* for x20 find M, (v), m, and m,.

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Q: 6. Find the median of an exponential random variable X with parameter 1 = 4. (The median of X is m…

A: Given : λ = 4 The density function for the exponential distribution. fx =λ×e-λ×x we know that the…

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

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!