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

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: Company A claims that the variance of the life of its appliances is less than the variance of the…

A: Company A claims that the variance of the life of its appliances is less than the variance of the…

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: Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero…

A: Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero…

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a normal random variable…

A:

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.

A:

Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

A:

Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

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: Let X be a normally distributed random variable with mean 600 and variance 10,000. Find two values…

A: Given Information Mean µ = 600 Variance V(x) = 10000 Standard deviation is given by

Q: If X is a Poisson variate such that 4) + 90 P(X=6), find the P(X=2)=9P variance (X =

A:

Q: If X is a Gaussian random variable with mean zero and variance o, find the pdf of Y = \XI.

A:

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: Find the standard deviation of a discrete random variable X which satisfies P(X=1)=0.1,P(X=-1)=0.6,…

A: Given: A discrete random variable X satisfies the following:     P(X=1)=0.1P(X=-1)=0.6    P(X=2)=0.3

Q: The number of cracks that need repair in a section of interstate highway follows a Poisson…

A: For a discrete random variable X ~P(m) the pmf is given as :   P(X=x) = e-mmxx!      , x=0,1,2,3,...…

Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

A:

Q: 1.28 On any day, the number of accidents on the highway has a Poisson distribution with parameter A.…

A: We  have to find mean and standard deviation for given uniform distribution...

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…

A:

Q: In the 2012 presidential election, exit polls from the critical state of Ohio provided the following…

A: As per our guidelines, we are allowed to answer first question only. Thanks   Given Data :

Q: Let xy X2 ..., Xn be a random sample from a Poisson distribution with parameter A. Find ML estimator…

A: ANSWER:  For the given data,

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

A:

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

A:

Q: Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the…

A:

Q: The probability distribution of the discrete random variable X is 3-x x = 0,1,2,3. .4, Find the…

A: Solution-: We have the p.m.f. of X is given by,  f(x)=3x*(14)x*(34)3-x f  ;  x=0,1,2,3;   We find…

Q: Determine the mean and the variance of X.

A: Given that  f(x) = 0.125 x    for 0&lt;x&lt;4   We know that  Mean = E(x) = ∫x.f(x) dx variance V(x)…

Q: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…

A: The given pdf is shown below:

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

A:

Q: Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the…

A: Given data: Mean = 6 Variance = 4 Thus, Std. Dev = sqrt(variance) = sqrt(4) = 2

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!