Suppose X₁ is a random variable which takes values (x₁,x) and X₂ is a randomvariable which takes values (x,x). Below is the table with values for joint probabilityP(X1, X2):x2 0.3 0.1x20.4 0.2which of the following statements is correct?A: P(X₁ = x₁, X₂ = x₂) = 0.3, B: P(X₁ = x₁) = 0.4, C: P(X₂ = x₂) = 0.2.Consider a coin experiment, where out of 10 trials, 3 successes were observed. Supposethat the Beta-Binomial model (with a uniform prior) was selected to fit the data. Whichof the below is TRUE?Hint: Recall that the Probability Mass Function (PMF) for the Binomial distributionis P(x = k)n!(n- -k)!k!!Beta distribution is F-1 (1-0)³–¹1)T(a+B)T(a)r (3)=0k (1 – 0)n—k, and the Probability Density Function (PDF) for theA: posterior p(x) ∞ Beta(4,8)B: posterior p(x) x Beta(12,5)

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Answered: Suppose X₁ is a random variable which…

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 probability generating function for a random variable X is given by: 1 1,25 1 9x(z) =z2 + 1 -z20 710 + 2 P(X < 5 |X < 13) equals Select one: а. 0.8 b. 0.2 C. 1 d. 0.286 е. О
Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (*) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X=2N -2. The values of X are given in the table below. Outcome ttt hth tht htt thh hhh hht tth Value of X -2 2 0 0 2 4 2 0 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the valuesof X. Then fill in the appropriate probabilities in the second row. Value x of X ___ ___ ___ ___ P(x=x) ___ ___ ___ ___
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 tth, then N (tth)=2. Suppose that the random variable X is defined in terms of N as follows: X=N²-2N-2. The values of X are given in the table below. Outcome ttt htt hhh tht tth hth hht thh Value of X 1 -2 -2 -2 -2 -3 -3 -3 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 0 0 0 00 X Ś
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
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
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 R be the random variable counting the number of heads in each outcome. For example, if the outcome is tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below. Outcome htt tht hth thh ttt hhh hht tth Value of X −6 −6 −6 −6 −4 −4 −6 −6 Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.
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 R be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then R(ttt) = 0. Suppose that the random variable X is defined in terms of R as follows: X= 2R- 4R-4. The values of X are given in the table below. Outcome ttt tth hht thh tht hhh htthth Value of X -4 -6 -4 -4 -6 -4 Calculate the values of the probability distribution function of X, i.e. the function py. 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 Px (x) olo
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