Consider another ubiquitous probability-course urn containing well-mixed black and white balls. There are15 balls in total, 5 white and 10 black. 3 are chosen, one at a time and at random. Let X; be 1 if the ith ballselected is white, and 0 otherwise.For parts (a) and (b), assume that the balls are selected without replacement.(a) Calculate the conditional probability mass function X1 given that X2 = 1.PX1 X2 (01) =PX1 X2 (1/1)10 415 14353515(b) Calculate the conditional probability mass function X1 given that X2 = 0.PX₁x2(0|0) =PX₁x₂ (10) =For parts (c) and (d), assume that the balls are selected with replacement.(c) Calculate the conditional probability mass function X1 given that X2 = 1.PX₁ X2 (01)PXX, (1/1)=(d) Calculate the conditional probability mass function X1 given that X2 = 0.PX₁x2(0/0) =PX₁ X2 (10)=Note: You can earn partial credit on this problem.

Step 1:(a) Calculate the conditional probability mass function PX1∣X2(x1∣1):Given that the balls…

Answered: Consider another ubiquitous…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The element titanium has five stable occurring isotopes, differing from each other in the number of neutrons an atom contains. If X is the number of neutrons in a randomly chosen titanium atom, the probability mass function of X is given as follows: 24 25 26 27 28 х 0.0541 p(x) 0.0518 0.0825 0.0744 0.7372 Find Hx- a.
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An unfair coin with Pr[H] =0.4 is flipped. If the flip results in a head, a marble is selected at random from a urn containing two red and eight blue marbles. Otherwise, a marble is selected from a different urn containing five red and three blue marbles. If the selected marble selected is red, what is the probability that the flip resulted in a head?
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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N² − 6N-1. The values of X are given in the table below. Outcome thh tth hhh hth ttt htt hht tht Value of X-5 -5 -1 -5 -1 -5 -5 -5 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 00 X
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