Let X ~ Binomial(3,0.5) and Y ~ Poisson(2) The two random variables are independent. Calculate the quantity, Var(2X-5Y)

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Q: 11- Consider the sample space S= {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}, where each point is…

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Q: Let the random variable Y = a + bX. Then, µy = bux. O True O False

A: Given statement isY=a+bX

Q: For events A and B we have P(A) = 0.3, P(B) = a and P(AUB) = 0.7. Then the value of a if A and 4. B…

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

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Q: Find the probability of event {X ≤5.5} for a Gaussian random variable having #x Ox=2. = 3 and

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Q: Let X(n,p) denote a binomial random variable with parameters n and p. Show that X(n+1,p)>=st X(n,p).

A: Given To prove that

Q: Given a binomial random variable, X-B(8,0.2). Compute P(X between 3 and 7). * Your answer Given a…

A: Note: Since you have posted questions with multiple subparts we will solve the first three questions…

Q: For a uniform random variable U∼U(2,11)U∼U(2,11), find the probability P(U<9)P(U<9): P(U<9)=P(U<9)=…

A: GivenA random variable x~Uniform(2,11)f(x)=1b-a      ; a&lt;x&lt;bf(x)=111-2f(x)=19  ;…

Q: a) Give the law of probability of Y and its parameters. b) What is the probability that Y is greater…

A: x1 ~ N(20,25) x2 ~ N(8,8)   The distribution of the mean of x1 is  x1 ~ N(u,σn)  x1 ~ N(20,2516) x1…

Q: 5. Let X and Y be independent random variables such that X - exp(A) and Y ~ exp(). (a) What is the…

A: It is an important part of statistics. It is widely used.

Q: Random variable X is uniform distributed in (- 1,3), EIX)

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Q: Exercise 28 Let X - Binom(16, ) and Y ~ Geom() be two independent random variables. Compute (i) E(X…

A: As by company policy I have solved first three part of this question....

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

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Q: the next season, and ave a the next season.

A: From Poisson distribution as, PX=a=e-nnaa!

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A: Poisson approximation is given by:

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A: Given : X¯=0Y¯=-1X2¯=2Y2¯=4RXY=-2W=2X+YU=X-3Y

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Q: Where does the z=2 come from? Just from X, and Y also being random variables?

A: Solution of the asked question is in step below.

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A: SOLUTION: Cov(X,Y)=np(1-p)-1

Q: X given Y.   Y=0 Y=1 Y=2 Y=3 Y=4 X=0           X=1           X=2

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Q: Assume 2 independent Binomial random variables, X- Binom(nx , P) Y ~ Binom(ny , P) Part 1: Derive…

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Q: Suppose X and Y are independent random variables with X - B (n, p) and Y ~ B (m, p). Show that X +Y…

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Q: If X is a random variable in the range 1≥x≥0, and f(x) = k(x^4-2), then the value of k is 1- 3/5…

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

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!