We have a 10-character sequence where a machine selects each character of the sequence independently and uniformly at random from {a, b, . . . , z}∪{A, B, . . . , Z}∪{0, 1, . . . , 9}. (a) What is the probability that exactly 6 of the characters are digits? (b) What is the expected number of digits in a sequence? (c)What is the variance of the number of digits in a sequence?

Q: random vanable x is normally distributed P(x<86) P(x<86)= (Round to four decimal places as needed.)…

A: X~N( μ , ?)μ=90     , ?=4Z-score =( x - μ )/?

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A: There are total 151 students &amp; Bus carry respectively 35,41,31,44 students.

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Q: A​ single, six-sided die is rolled. Find the probability of rolling an odd number or a number less…

A: A single six sided die is rolled.Sample space S = {1, 2, 3, 4, 5, 6}Odd number or less than 4 = {1,…

Q: Use the Peano Axioms to prove each of the following. (a) 12 • (b) 1 3 and 2 = 3 ●

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A: It is required to estimate the number of pistons in the sample that are defective using the mean,…

Q: 1. Let X, Y be non-negative continuous random variables with probability density functions (pdf)…

A: X and Y are independent

Q: A fair coin is tossed three times. What is the probability that all three tosses are tails? Write…

A:

Q: If p= 1.2% and n = 500, is the Poisson distribution a reasonable approximation of the binomial…

A: Given that p = 1.2% and n = 500,we are asked whether the Poisson distribution is a reasonable…

Q: 1. A random variable X has expectation E(X) = μ and variance o². Suppose that Z = a) Compute E(Z).…

A: Given that X is a random variable with expectation  and variance .Suppose that

Q: d) Find P(27060 ≤ (X-500)² ≤ 50240). e) Find the mean of (X - 500)², i.e. E ((X - 500)²).

A:

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A: 5 different colored flagsWe need to select 5 flags from 5

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Q: What is the probability of a group having an average high school GPA below 4.1? In 2019, the average…

A: Mean()=4.32standard deviation()=0.285sample size(n)=25

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A: From the provided information,

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A: Z be the standard normal distribution Z~N(0,1)

Q: (b) What is the probability that you purchase at least 9 boxes?

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Q: Consider the unit cirlce in the plane; that is, the set of all points within a distance of 1 of the…

A:

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A: 4 red marbles, 3 green ones,2 white ones,1 purple one

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Q: What is the expectation of X?

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A: The joint probability distribution of the random variables is

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A: If 8 distinct dice are rolled than the possible out comes are 68 .

Q: What numbers do you plug in the formula to get $18.22?

A: Given that E(X) = 18.22

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Q: random variable X is given in the following table. Find the standard deviation of the random…

A: PMF of Xx-2-1012P(X =x)0.160.170.300.150.22

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Q: Y 1 x 0 2 3 0 0.04 0.09 0.10 0.12 1 0.07 0.11 0.08 0.04 0.15 0.10 0.05 0.05 2 (a) Compute E(X),…

A: Suppose the joint pmf of X and Y is

Q: What is the expectation of X?

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Q: 2. A Markov chain has the following transition matrix ||1/3 1/3 1/3|| P = 1/3 2/30 1/3 0 2/3 a. Draw…

A:

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A: Given the joint probability distribution for the rates of return for the stock prices of the two…

Q: In each case, determine the value of the constant c that makes the probability statement correct.…

A: Mean=0Standard deviation=1