Consider the joint probability mass functionPerson 1 inPxr(x, y)Person 2 inSeat 1Seat 2Seat 3Seat 4Seat 5Seat 10.030.040.060.08Seat 20.030.080.050.04Seat 30.040.080.030.07Seat 40.060.050.030.02Seat 50.080.040.070.02а.What is the probability that Person 1 is in a seat next to Person 2?b. Find the marginal pmf of X, px (x)Find the marginal pmf of Y, py (y)с.d. Are X and Y independent? You must demonstrate this using the definition.What is the correlation between X and Y?What is the conditional probability that Person 1 is in seats 1 or 2 given Person 2 is in seat 3?е.f.

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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The joint probability mass function of Xand Ylis given by p(1, 1) = 0.2 p(2, 1) = 0.1 p(3, 1) = 0.05 p(3, 2) = 0.1 Р(1,2) - 0.1 p(2, 2) = 0.05 p(2,3) 0.05 p(1, 3) = 0.1 p(3, 3) = 0.25 %3D (a) Compute the conditional mass function of Ylgiven X 2: P(Y = 1|X = 2) D %3D P(Y = 2|X 2)= P(Y 3|X = 2) (b) Are Xland Yindependent? (enter YES or NO) NO
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O 31 75% i 2:02 pm exam.ptuk.edu.ps/mod/ 19 احتمالات عبد ال له Let X be a continuous random variable with probability density function -1
Let X , Y be two random variables with the following joint probability mass function: X/Y 2 6 -2 8 -2 0.109422 0.0270663 0.0223591 0.0600166 3 0.120172 0.0297199 0.0245512 0.0659006 -7 0.139485 0.0344963 0 0.0764918 4 0.130901 0.0323734 0.0552402 0.0717846 a.) Are X and Y independent?
Suppose that the moment-generating function of a random variable X is given by Mx(1) = +" +" + 4 3t 2 4 5t 15 Find the probability mass function of X.
Let X and Y be two random variables with joint probability mass function: p(x,y) = xy(1+y) for X=1,2,3 and Y=1,2 p(x,y) = 0, Otherwise. Please enter the answer to 2 decimal places. • What is the variance of (4-5X)?
The service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?
another random variable Y. The joint probability masS function of X and Y is dter random variable Y. The joint probability mass function of X and Y is listed below. am put to a communication channelis a random variable X and the output is Y/X -1 1/4 1/8 -1 Р (Х, Y) %3D 1/4 1 1/8 1/4 Find (a) P (Y=1/X=1) (b) P (X=1/Y=1)
8
c) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.
Please helpt to solve this. Can you handwrite the solution please? It helps to follow the steps properly. Thank you!

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