2. If the random variable Xhas the probability density function ƒ(x) = ³(1 − x²), −1 < x < 1, what is the variance of 15X + 2?

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: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

Q: Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y…

A:

Q: Suppose that X ~ Pareto(y). Define Y = In(X+1). If E[X] = , then what is the variance of Y? %3D %3D

A: For X~Pareto(γ), if x∈(0,∞) then the probability distribution function(pdf) of X is given by…

Q: 5. Let X have the pdf {(x + 1) -1 <x < 1 f(x) = elsewhere. Find the mean and the variance of X.

A: 5. The given pdf is, fx=12x+1       -1&lt;x&lt;10                   elsewhere

Q: If the probability density of X is given by f(x) =2x−3 for x &gt; 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: Suppose that X and Y are independent random variables having the joint probability distribution:…

A: Joint Probability Distribution: Let there are two random variables X and Y. Then the joint…

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.

A:

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

A:

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

A:

Q: 2Y 0 Show that has a x² distribution with 2 degrees of freedom.

A: Mean =θ ,

Q: arger variance. lom variable X be the height of a random CS500 at from the same group in…

A: True

Q: b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

A:

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

A:

Q: What did you learn from binomial and hyper geometric distributions? Write a brief note of five lines…

A: Binomial distribution: Consider a random experiment involving n independent trials, such that the…

Q: Let D denote the event that a subject has a certain disease. Let S denote the event that a subject…

A: Given: P(D|x) = exp(α+Xβ) / (1+exp(α+Xβ)).

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

A: given dates  p ( cancer) = 0.03 n = 10 patients  q = 1=p = 1-0.003 = 0.997

Q: Let X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random…

A:

Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

A: Given that Z is a continuous random variable having a distribution Erlang with parameters (…

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

A:

Q: If E denotes the expectation (random variable X is denoted the variance of a as (E(X))^2 - E(X False…

A: Given,E denotes the expectation .

Q: The variance of a discrete probability distribution can be calculated using the formula: H=Ex.p(x)…

A: We know that  E(x)= ∑X.p(x)E(x2 ) = ∑X2.p(x)Variance =?2 = E(x2 ) - [E(x)]2 Where μ= E(x)

Q: Suppose the probability function for x is such that p(x=1)=0.3, p(x=2)=0.4 and p(x=3)=0.3. What 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: If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.

A:

Q: Let Y be an exponential random variable with (unknown) mean 0.

A: Mean of Y is θ

Q: A random variable X takes value 1 with probability and the value 2 with the remaining probability.…

A: The total probability of any probability distribution is always 1.

Q: Suppose that X₁, ..., Xn are i.i.d. from a normal population with mean µ and variance o². Calculate…

A: Let X1,X2​,…,Xn​ be independent and identically distributed (i.i.d.) random variables from a normal…

Q: 2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard…

A:

Q: . Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Here, we have,  E[X] = 0 P(-3&lt;X&lt;2) = 1/2  Now, P(-2&lt;X&lt;2) = 1/2 (Since, X cannot be…

Q: The random variable X takes value O with probability, and value 1 with the remaining probability.…

A: We have given information, The random variable X takes value 0 with probability 13, and 1 with…