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To find the variance of a hyper geometric random variable in Equation 2.5-2, we used the fact that
Prove this result by making the change of variables
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Chapter 2 Solutions
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward(16) The moment-generating function of the geometric random variable X with parameter p is M(t) = 1-per. Use this to find the mean and variance of X.arrow_forwardIf X₁, X2,..., Xn constitute a random sample of size n from an exponential population, show that X is a sufficient estimator of the parameter 0.arrow_forward
- Example 24: If a random variable X has the moment generating function Мx (t) — 2-t' determine the variance of X.arrow_forwardSuppose that a random variable X has the following moment generating function, < ¼/7. MX(t) = = (1-9t)−7, t< (a) Find the mean of X. (b) Find the variance of X.arrow_forwardProve that the variance of b, V(b) = o²(X'X)−¹arrow_forward
- Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is the expected value of the random variable X and varX = E(X - μ)^2 is the variance of the random variable X. Guidance: start from the representation - (X-a)^2 = (X µ + μ- a)^2 and group the right side of the representation appropriately into the form (Z + b)^2, where Z is some random variable and b is a real number and open the square. The task should be solved with the help of the expected value calculation rules.arrow_forwardProb. 3 Let X be a random variable with cumulative distribution function (cdf) given by (1-e-x², x ≥ 0 ={1,- x<0 Find the probability that the random variable X falls within one standard deviation of its mean. Fx (x) =arrow_forwardshow all solution 1. Suppose X is a random variable with E(X2)=10 and E(X)=2. Find the following: a) E(2X + 5) b) Var(X) c) Var(2X + 5) d) Var(2X – 5)arrow_forward
- 2arrow_forwardSuppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., X₁ has the following probability density function (exe-e x! 0, f(x; 0) = for x = 0,1,2,... elsewherearrow_forwardIf Y is an exponential random variable with parameters beta then mean = E(Y) =beta and variance squaared = V(Y) = beta squared. Show proof of thisarrow_forward
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning