Let X1, X2, ... , X100 be 100 i.i.d.r.v.s. with mean 70 and variance 64. Find the probability that the sample mean (Xbar) is less than 72. That is find P{ [ (X1 + X2 + ... + X100) /100] < 72 }.
Let X1, X2, ... , X100 be 100 i.i.d.r.v.s. with mean 70 and variance 64. Find...
Let x1, x2, . . . , x100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 25 lb and variance 1 lb2. Let x be the sample mean weight (n = 100). (a) What is the probability that the sample mean is between 24.75 lb and 25.25 lb? (Round your answer to four decimal places.) P(24.75 ≤ x ≤ 25.25)...
24. Let X1, X2, ...., X100 be a random sample of size 100 from a distribution with density for x = 0,1,2, ..., otherwise. What is the probability that X greater than or equal to 1?
Let x1, x2, x3,...,x100 denote the actual weights of 100 randomly selected bags of fertilizer. Let X be the average weight of this sample. If the expected weight of each bag is 50 lb. and the standard deviation of bag weights is known to be 1 lb., calculate the approximate value of P (49.75 ≤ X ≤ 50.25).
5. Let X1, X2,... , X100 be i.i.d. random variables, following the normal distribution N(0, 102). Let α denote the probability that there are at least 3 variables among them whose absolute value is larger than 19.6. Compute α, and give an approxi- mate value of α with an error less than 0.01 according to the Poisson distribution. 15pts] 5. Let X1, X2,... , X100 be i.i.d. random variables, following the normal distribution N(0, 102). Let α denote the probability...
Let X1 be a normal random variable with mean 2 and variance 3, and let X2 be a normal random variable with mean 1 and variance 4. Assume that X1 and X2 are independent. What is the distribution of the linear combination Y = 2X1 + 3X2?
Suppose X1, X2,..., X10 are independent normal random variables with mean O and variance 1. Let max{X1, X2, ..., X10} What is the largest value of t so that P(M <t) < 0.90? That is, find the 90th percentile of M.
Suppose X1, X2,..., X10 are independent normal random variables with mean O and variance 1. Let max{X1, X2, ..., X10} What is the largest value of t so that P(M <t) < 0.90? That is, find the 90th percentile of M.
Suppose X1, X2,..., X10 are independent normal random variables with mean O and variance 1. Let max{X1, X2, ..., X10} What is the largest value of t so that P(M <t) < 0.90? That is, find the 90th percentile of M.
Suppose X1, X2,..., X10 are independent normal random variables with mean O and variance 1. Let max{X1, X2, ..., X10} What is the largest value of t so that P(M <t) < 0.90? That is, find the 90th percentile of M.
Suppose X1, X2,..., X10 are independent normal random variables with mean O and variance 1. Let max{X1, X2, ..., X10} What is the largest value of t so that P(M <t) < 0.90? That is, find the 90th percentile of M.