a) Two events, M and N, are such that P(M) = 0.6, P(M NN) = 0.2, P(M UN) = 0.85 Find P(N \M) State, with reason, whether M and N are mutually exclusive independent. (i) (ii) (iii)

Q: Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An…

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

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Q: 1 1 Let A and B be independent events with P(A)= and P(B)= 5. Find P(An B) and P(AUB). 7 P(ANB)= ***

A: given data P(A)= 18P(B) = 15independent eventsfind P(A∩B)and P(A∪B)

Q: Event A and event B are mutually exclusive, P(A) = 0.6 and P(B) = 0.2 Calculate the following,…

A: Answer: From the given data, P(A) = 0.6  P(B) = 0.2 Event A and event B are mutually exclusive,

Q: 2. Let X be a geometric random variable with parameter (the success probability) p. Let Ak be the…

A: It is provided that X be a geometric random variable with parameter (the success probability)…

Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.

A: Proof: PA=PA∩A=PAPA  Since A is independent itself.⇒PA1-PA=0PA=1  Since P(A)>0

Q: 1. We have an urn with 15 red, 20 blue and 25 green balls. (a) We draw 10 balls without replacement…

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Q: Suppose that you have 9 cards. 4 are red and 5 are purple. The cards are well shuffled. You randomly…

A: As per the guidelines we are allowed to solve maximum of 3 subparts If you need help with another…

Q: Let B1, ... , Bn be independent events. Show n n P(ÜB.) = 1- T1c (1— Р(B,)). i=1 1=1

A: P∪I=1nBi=1-∏i=0n1-PBi For n =1             R.H.S=1-(1-PB1)=1-1+PB1=PB1=L.H.S For n = 2…

Q: Suppose all 8 possible outcomes of an experiment are equally likely and denoted as E1, E2, E3, E4,…

A: Given that, the 8 possible outcomes are equally likely events. So, the probability…

Q: For any two events A and B it is known that P(A) = 2/3, P(AUB) = 7/12 and P(A∩B) = 5/12, find P(B

A:

Q: Which of the following is NOT true:

A: Here given different sentences for probability .

Q: Suppose that you have 9 cards. 4 are red and 5 are purple. The cards are well shuffled. You randomly…

A: Solution: Given that there are 9 cards. 4 are red and 5 are purple cards. Two cards are randomly…

Q: Q.4. Compute the probability that: (a) their sum is odd; (b) their product is even. Four distinct…

A: Given : Four distinct integers are chosen at random from the first 10 positive integers. In the…

Q: B. Find the value of n: (n+3)t 1. (n+1)! = 20

A:

Q: ppose that you have 10 cards. 4 are blue and 6 are orange. The cards are well shuffled. You randomly…

A: a) P(B1 AND B2) = 410 x 39 = 0.13   b)P(At least one blue) =1 - P(no blue) P(At least one blue) =1 -…

Q: Let (Xn)neN and (Yn)neN be two sequences of random variables and X and Y some random variables.…

A: Given that Xnn∈N and Ynn∈N be two sequences of random variables and X and Y some random variables.

Q: Generalisation. The mathematical expectation of the product of a number of independent random…

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Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

A:

Q: Probability of event s1 = 0.21, probability of event s2 = 0.17, probability of event s3 = 0.39,…

A: Given thatP(s1)=0.21P(s2)=0.17P(s3)=0.39P(s4)=0.23Suppose that t = {s2 union s4}.

Q: Three students scheduled interviews for summer employment at the Brookwood Institute. In each case…

A: We have given information, Three students scheduled interviews for summer employment at the…

Q: Three students scheduled interviews for summer employment at the Brookwood Institute. In each case…

A: a) Experimental outcomes are defined in terms of the results of each student interview. (Let Y = the…

Q: 1, k‡ j − ¹, j, j +1} are independent. (In other words, X; might be dep X₁-1 and Xj+1, but is…

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Q: Three coins are tossed. n(S)= Events: (a). the first coin shows a T n(a)- P(a)- (b). there are at…

A: given experiment: three coins are tossed.

Q: A student stays at home. Let event N = the student watches Netflix. Let event Y = the student…

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Q: The following models were proposed for a binary response y and explanatory variables x1,x2,x3 ,…

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Q: a) Two events, M and N, are such that P(M) = 0.6, P(M nN) = 0.2, P(M UN) = 0.85 Find P(N |M) State,…

A:

Q: Theorem 3-7. For n events A, Az, ..., Ag, we have P(U a) = E P(A.) – EE P(A, n A) + EE P(A;nA;nAd)…

A:

Q: Suppose that P(A;) = 1 for all i = 1, 2, .... Show that P(N A;) = 1.

A:

Q: 8Given that p(A | B)=0, and p(A)=.15, (a) independent? (b) exclusive? are A and B

A: we know that if two events A and B are independent thanP(A|B)=P(A)and P(B|A)=P(B)  If two events A…

Q: A fair coin is tossed three times. Let R, S and T be three events R: maximum one coin shows tail, S:…

A: Solution: A fair coin is tossed three times. The sample space Ω is  Ω= { HHH, HHT,…

Q: P(13,5) for P(n,r)= n!/(n-r)!

A: find out P(13,5) using formula

Q: 5. Let X be a nonnegative, integer-valued random variable. (a) Simplify X-1 as 0.) (b) Simplify…

A:

Q: . The probability that two specified letters will be placed in the correct envelopes is 1[n(n – 1)].…

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Q: Statement. For n events A, Az, ..., Ag, we have A₂, 'n' n (α) 0) P(24) 2 | > ΣΡ(4)-(n-1) i=1 η ομώνα…

A:

Q: Theorem 3-8. For n events A1, A2, ..., A„ 11 P( 4)> U A; 2 E P (A;) – E P (A;^ A) i = 1 i = 1…

A:

Q: Compute the following Probabilities Pris distributed N (4,9), P. (YS6) = 4 if Y is dis tributed…

A: 1a) ∑axi+b = a∑xi+∑b  =a*n*x + n*b therefore option ii is the correct option

Q: m 2 and P(D) = 3 Find 10 Events C and D are mutually exclusive such that, P(C) = (a) P(C') (b)…

A: Given P(C) = 25  and  P(D) = 310