IIT JAM Exam > IIT JAM Questions > Let X1, X2 and X3 be i.i.d. U(0,1) random var...
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Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equals
- a)1/6
- b)1/4
- c)1/3
- d)1/2
Correct answer is option 'A'. Can you explain this answer?
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Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2...
To find P(X1 < x2="" />< x3),="" we="" need="" to="" find="" the="" probability="" that="" x1="" is="" less="" than="" x2="" and="" x3="" is="" greater="" than="" />
Let's break down the problem into two parts:
1. P(X1 < />
Since X1 and X2 are independent and uniformly distributed between 0 and 1, the probability of X1 being less than X2 is 0.5.
2. P(X3 > X2)
Since X2 and X3 are independent and uniformly distributed between 0 and 1, the probability of X3 being greater than X2 is also 0.5.
Since these two events are independent, we can multiply the probabilities to get the final probability:
P(X1 < x2="" />< x3)="P(X1" />< x2)="" *="" p(x3="" /> X2) = 0.5 * 0.5 = 0.25.
Therefore, the probability that X1 is less than X2 and X3 is greater than X2 is 0.25.
Let's break down the problem into two parts:
1. P(X1 < />
Since X1 and X2 are independent and uniformly distributed between 0 and 1, the probability of X1 being less than X2 is 0.5.
2. P(X3 > X2)
Since X2 and X3 are independent and uniformly distributed between 0 and 1, the probability of X3 being greater than X2 is also 0.5.
Since these two events are independent, we can multiply the probabilities to get the final probability:
P(X1 < x2="" />< x3)="P(X1" />< x2)="" *="" p(x3="" /> X2) = 0.5 * 0.5 = 0.25.
Therefore, the probability that X1 is less than X2 and X3 is greater than X2 is 0.25.
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Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer?
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Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer?.
Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X1, X2 and X3 be i.i.d. U(0,1) random variables. Then P(X1 > X2 + X3) equalsa)1/6b)1/4c)1/3d)1/2Correct answer is option 'A'. Can you explain this answer?.
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