Let the three mutually independent events C₁, C₂, and C3 be such that P(C₁) = P(C₂) = P(C3) = 1/4. Find P((C₂NC₂UC₂).
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A: A and B are disjoint. This means, that: PA∩B=0
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Q: Find a value of c so that P(Z ≤ c) = 0.74.
A: Find a value of c so that P(Z ≤ c) = 0.74.
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A: It is given that:And, A and C are independent events.
Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?
A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).
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Q: For events A and B, prove that P (An B) >1– P (Aº) – P (Bº).
A: We want to prove the above result. Result: 0≤P(A)≤1
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Q: Find P(U or V)P(U or V).
A: Concept: Two events are said to be mutually exclusive if both the events cannot occur at the same…
Q: J and K are independent events. P(J | K) = 0.17. Find P(J) P(J) =
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Q: J and K are independent events. P(J | K) = 0.76. Find P(J) P(J) =
A: Solution: Independent events: Two events A and B are said to be independent if the happening of one…
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A: The probability of an event is the chance of occurrence of that event.
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Q: Consider events C and D, such that P(C′)=0.6, P(D′)=0.4 and P(C∩D)=0.3. Find P(C|D)
A: Given that, P(C′)=0.6 P(D′)=0.4 P(C∩D)=0.3
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A: Given, The objective is to find the P(J).
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Q: State whether the standardized test statistic t indicates that you should reject the null…
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Q: Let A and B be events such that Pr[A]=0.37, Pr[B]=0.62, and Pr[A N B]=0.11. Find Pr[A|B].
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Q: Consider the linear probability model Y; = B0 + B1X¡ +ui, and assume that E(ui| Xi) = 0. (a). Show…
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Q: J and K are independent events. P(JK) = 0.3. Find P(J).
A: Two events J and K are given.
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A: A and B are the Independent Event if P(A ∩ B) = P(A) P(B)
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A: From the provided information,
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Q: For this problem, assume that Pr[A∪B]=0.85 and Pr[A]=0.5Pr[A]=0.5. What is Pr[B] if A and B are…
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Q: J and K are independent events. P(J | K) = 0.23. Find P(J)
A: From the provided information, J and K are independent events and P(J|K) = 0.23
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- Let E and F be events in an experiment. If P(E|F)=0.5, P(E|F')=0.2 ,and P(E∩F')=0.1, find P(F) and P(E).Q1 Let X1 and X2 be independent exponential random variables with identical parameter A. Q1(i.) Find the distribution of Z = max(X1, X2). Q1 (ii.) Find the distribution of Y = min(X1, X2). Q1(iii.) Calculate E[Y]. Q1(iv.) Calculate E[Z]. Q1(v.) Using the relation Z = X1+X2 – Y, Calculate E[Z] and verify that it agrees with the calculation done in part (iv.)K:56) Somehow you manage to build a fair 3-sided die, equally likely to show 1, 2, or 3 every time it is rolled. You roll the die twice, with the results each time being independent. If X is the maximum of the 2 numbers rolled and Y is the sum of the 2 numbers rolled, find the correlation ρ(X, Y ).
- State whether the standardized test statistict indicates that you should reject the null hypothesis. Explain. (a) t=1.538 (b) t=0 (c) t= 1.489 (d) t= - 1.574 tents esour =1533 ccess (a) For t= 1.538, should you reject or fail to reject the null hypothesis? uccess O A. Fail to reject Ho, because t> 1.533. O B. Reject Ho, because t 1.533. Options O D. Fail to reject Ho, because t< 1.533.2. Let X and Y be independent random variables with E[X] = 4, Var[X] = 84, E[Y] = 6, and Var[Y] = 54. Find E[5X + 2Y - 18] - b. Find E[-3Y+X+3] -a. -с. Find E[X2] d. Find ox e. Find E[Y2] f. Find Oy g. Find Var[X+3Y - 6] h. Find Var[3X - 2Y + 35] Find E[(2X - 8)/5] j. Find Var[(2X - 8)/5] i.Let X₁, X2, X3, be a random sample from a discrete distribution with probability function p(x) = for x = 0, for x = 1, otherwise. Determine the moment generating function M(t) of Y = X₁X₂X3- A. exp(t) B. (exp(t)+7)/8 C. (exp(1/2)+1)/3 D. (exp(t)+63)/64 E. (exp(t)+1)/4
- A student goes to the library. Let events B= the student checks out a book and D= the student check out a DVD. Suppose that P(B)=0.54 P(D)=0.45 and P(D|B)=0.50 Round each answer to four decimal places. (a) Find P(B′)Enter the exact answer.P(B′)= (b) Find P(D AND B)Enter the exact answer.P(D AND B)= (c) Find P(B|D).Round your answer to three decimal places.P(B|D)= (d) Find P(D AND B′)Enter the exact answer.P(D AND B′)= (e) Find P(D∣B)Enter the exact answer.P(D∣B′)2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. (a) Find P(X1 = 2 and X2 = 2). (b) Find P(X1 + X2 = 1). (c) Find E(X1 + X2). (d) Find Var(X1 + X2).Consider the following scenario: • Let P(C) = 0.3• Let P(D) = 0.8• Let P(C|D) = 0.3 A. P(C AND D) = [ Select ] ["0.30", "0.24", "0.26", "0.11"] B. Are C and D Mutually Exclusive? [ Select ] ["No, they are not Mutually Exclusive.", "Yes, they are Mutually Exclusive."] C. Are C and D independent events?[ Select ]["No, they are Dependent.", "Yes, they are Independent."] D. P(C OR D) = [ Select ] ["0.92", "0.86", "0.60", "1.1"] E. P(D|C) = [ Select ]["0.30", "0.95", "0.24", "0.80"]
- Let X; be random variables and M; (t) be their respective moment generating functions, for i = 1, 2, 3. Solve: Suppose that M₁ (t) = 1 +t+t² + t³+... Is this enough information to determine the type of random variable that X₁ is? Explain why or why not. Determine the type of random variable if there is enough information. Determine if it is possible for M₂ (t) = (-1)" -0 (2n)! possible, determine the type of random variable that X₂. -+2n. Explain why or why not. If it is Suppose that that the expectation of X3 is -1 and its second moment is 1. Determine if this is enough information to find the moment generating function of X3 explicitly. Explain why or why not. If it is enough information, compute it explicitly.Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with that of pX(x) if pX(x)=1/3,x=−1,0,1, zero elsewhere