A random variable X takes values 1,2,3,. . with probability mass function r! r= 1, 2, 3, . .o. Find the value of 2.
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- Prof that' For a fixed B with P(B) > 0, P(A l B) is probability function.Let JO, J1,..., J4 independent random variables according to the Ber (r;) law, where i = 0, 1,..., 4, respectively. We define the random variables Xi = min {JO + Ji, 1}, for i = 1, 2, 3, (a) Find the law of Xi , for each i = 1, 2, 3, 4. (b) Find the law of (X1, X2, X3, X4).Q5 Let = {} 1 f(x) = x = 1, 2, 3, 4, 5, 6, otherwise. be the probability mass function of a discrete random variable X. Show that the probability mass function of the smallest observation Y₁ of a random sample of size 5 from this distribution is 5 91 (y₁) = = (²-")" - (0 =³) "₁ 6 6 y = 1, 2, 3, 4, 5, 6. and zero otherwise. Note: you already know how to write down the cumulative distribution function of Y₁, the smallest of X₁, X₂, X3, X₁, and X5; remembering that we are sampling from a discrete distribution, derive the probability mass function of Y₁.
- Let X ~ N(1,2) and Y ~ N(4, 7) be independent random variables. Find the probability P(X + Y > 0):72. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.
- The random variable X has the geometric distribution with probability mass function (pmf) Py(x) = q*p. x = 0,1, 2, ... 0 x). |A7 The random variable X has the binomial distribution with probability mass function () p*(1 - p)²-*, x = 0, 1,2; 0the probabilty of mass funtion of a random variable J is given as (picture)3 Let X be a random variable with probability Law P (X = r) = q, K for r = 1,2,3.. . 00, Find the moment generating function and mean of ihe random variable X. Let K+ q = 1.do fasta box contains 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?Depending on the input a computer program takes variable number of cycles to come up with the answer. Let X be the random variable which takes on the values k = 1,2,3,··· ,infinity for the number of cycles required to come up with the answer where 1 is the possibility that the program never arrives at an answer. (a) The probability mass function (p.m.f) for completing in k cycles is p_X(k) = (2^k)/(3^(k+1)) , k = 1,2,3,··· . What is the probability that the computer program never completes? (b) Use part (a) to find probability P (X greater or equal 3). Write your answer in a simplest fraction. (c) Given that the program has not found the answer after 2 cycles, what is the probability that it will never find the answer?SEE MORE QUESTIONS
