The random variable X and Y are independent. The random variable X has the probability distribution P(X=0) = 0.4 and %3D P(X=1) = 0.6. The random variable Y has the probability distribution P(Y=0) = 0.2 and P(Y=3) = 0.8. Fill the following Joint distribution table:
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- 9. Prove the formula: e* ≥ 1 + x, Vx € R. 10. What is the probability that in a random group of 10 people at least two have the same birthday? Consider the experiment: Two fair die are cast and the sum of the spots shown on the uppermostUsing the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.There are 7 balls hidden in a box (3 blue and 4 green). If you first select a green ball and do not replace in the box, what is the probability that the second ball you select from the box will also be green? [Your answer can be written either as a fraction or decimal]
- Size of sample space A six-sided dice is rolled, a five-sided dice is rolled and a three-sided dice is rolled. Considering this as a probability experiment, what is the size of the sample space? An Event In the context of the probability experiment just described (a 6-sided, a 5-sided, and a 3-sided dice thrown): Consider the event in which two face- up numbers on the three dice add to 10. What is the size of this set? Save ResetA and B stand in a line at random with 10 other people. What is the probability that there are exactly 3 people between A and B?Hypergeometric distribution Given user defined numbers k and n, if n cards are drawn from a deck, find the probability that k cards are black. Find the probability that at least k cards are black. INPUT 11 7 OUTPUT 0.1628063397551007 0.24927823677714275
- A coin is flipped 8 times in a row (assume all outcomes are equally likely). For each of the following questions, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. Q1.1 What is the probability that it lands on heads exactly four times?Write a function my_random that samples a random number from the following discrete probability distribution on the set {8, 9, 13, 15, 17, 18}: P({8}) = ²/ 9 P({9}) = ²/ 18 P({13}) = 1/ P({15}) = P({17}) = ²/ 16 NO P({18})= =X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.
- An Internet Service Provider opens 10 new accounts per day, on average. Let X be a random variable that returns the number of new accounts open in any given day. Answer the following questions; insert your answers as TwO decimals as in 0.xx: (a) The probability that on any given day there are at most 10 accounts open is (b) The probability that on any given day there are exactly 10 accounts open is (c) The expected number of new accounts over one week is (insert your answer as an integer, rounded to the nearest):You are given the following data: vocabulary V = {w1, w2, w3} and the bigram probability distribution p on V × V given by: p(w1, w1) = 1/4 p(w3, w3) = 1/8 p(w2, w2) = 0, p(w2, w1) = 1/4, p(w1, w3) = 1/4, p(w1, *) = 1/2 (that is w1 as the first of a pair), p(*, w2) = 1 /8 . Calculate p(w1, w2) and p(w2 | w3) using Markov's ruleThe probability of event A is 55%. The probability of event B is 40%. The probability that A happens given that B has happened is 25%. What is the probability that both A and B happen? 95% 70% 65% 10% 15%