(a) Determine c. (b) What is P({k}) now that you have determined c? (c) Compute P({k + 1, k + 2,...}) for k = 0, 1, 2,....

Q: Let n(B) = 5 and n(AUB) = 7. (a) What are the possible values of n(A)? (b) If n(An B) = 0, what are…

A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: Section I 3. Suppose that X is a discrete random variable with pmf |4- r|+ 4 f(z) for =-6,-3,0,3,6,…

A: Solution

Q: P(n) assert n(n+ 1)(2n + 1) j=1 (a) Verify that P(3) is true (b) Express P(k). (c) Express P(k + 1).

A: Consider the provided question, (a) We have to verify that P(3) is true. Substitute n = 3 in…

Q: Assume that P(A₁ N A₂ NA3) > 0. Prove that P(A₁ NA₂ NÃ3 Ñ A4) = P(A1)P(A2|A1₁)P(A3|A1 N A₂)P(A4|A₁…

A: We have conditional probabilitiesP() =       (i)P( =                       (ii)P( =…

Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

Q: 1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c)…

A: As per our guidelines we are suppose to answer only three sub parts.…

Q: Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a…

A:

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: compute (2A)T − (3B)T

A:

Q: k It is known that ( + (₁ ²₁₂) + (k) = (²+¹) (k + 1). Prove that r - 2 (k) + ( k + ¹ ) + ( k + ²) +…

A: We will use given formula and value of nr . nr=n!r!×n-r!

Q: Using the recursive relation I (r + 1) = r[ (r) and the fact that I ย relat 1 2 }} 5 {} and (b) £ =…

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Q: P(ANB) = P(A)NP(B).

A:

Q: 3- (a) Complete k (-1)k 2 k! (k +n+ 1)! 2k+n = -h(x) k=1

A: First I have written the Bessele's function as in an infinite series form then by making a…

Q: ( 9x2 4 if a 2 Let p(x) = 4x + 8 if a < 2 Compute the following values. (a) p(1) = (b) p(2)

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Q: Find the general solution of the recursive relation an ○ an = a (1 + √√14)” + ß(1 − √√14)” an = a(1…

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Q: 4n2 +14n +1 c. Let P(n):9+13+...+(4n+5) = Show P(k) P(k+1). Is P(n) true Vintegersn21? 10 Fon the…

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Q: k + 6 k+6 Hint: 126 = -te 3 Assume that n is a positive integer. Compute k+1 k3 + 3k² + 2k* k=1

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Q: (5) {1,2} C P({1, 2}).

A: Given  set is {1,2},  we knew that power set of a given set is set of all subsets of the given set.…

Q: Let f: AB and 9: B→C be defined as follows: f(a) = 4a² +2 and g(b) = 26-7 Compute the following: (a)…

A: Let A=B=C=x|x is a real number Let f:A→B and g:B→C be defined as  fa=4a2+2andgb=2b-7 Hence…

Q: Suppose X₁ ~ N(6, 1) and X₂ ~ N(7,2), and X₁ is independent of X₂. Find P(X₁ < X₂) and P(X₁ < X₂ +…

A: We know linear combination of normal distribution is also a normal distribution. Therefore any…

Q: P(A) = 0.6, P(B) = 0.4, P(A∩B)= 0.2 a) Find P(A given B)     b) P(B|A)

A: Given data: The given probability of A is P(A)=0.6. The given probability of B is P(B)=0.4. The…

Q: 1 = (₁ + - +/- ) ² (b) Prove that n < 1+ for all n € N.

A:

Q: Computek(k+1) k=1 Hint: Use the fact that Ek-1(ak-ak-1)= anao (this is called telescoping) and…

A: The given series .The aim is to compute the sum of the series.

Q: Supppose that X ~ N (2; 3). Find P (1 &lt; X &lt; 4).

A:

Q: If p(z) = (z-3)(z+4)(z-8) then find p(5)

A: