If Ac B, then P(A) < P(B).

Q: 5. A norm al distribution has a mean of 26 and a standard deviation ốf 4. What Is the probability…

A:

Q: In(x²) = 2 ln(x) for all x True O False

A: ln(x^2) =2ln(x) for all x

Q: The following is a valid identity, true or false? P(k): 1+2+22 +23 + .. +2k = (2(k+1)/2) +…

A:

Q: Supposer FCE, acE is algebraic F and dog (a/F) 13 odd. Proveo that F(a)= F(a²). over

A:

Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

A:

Q: Tiger Woods hits an average driver 287.2 yards with a standard deviation of 24.6 yards. What is the…

A: The probability value is calculate by means of standard normal variate with the random variable,…

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: iii. P(AN B) = P(A) N P(B). iv. P(A) UP(B) C P(AUB)

A:

Q: Suppose that x is N(15,4). Find the P(X>11).

A: The random variable X follows normal distribution. The population mean is 15. The population…

Q: If S = {a, b, c} with P(a) = 4P(b) = 3P(c), find P(a).

A:

Q: If In elnx - = In (x – 4) = In2, then x %3D

A:

Q: Find out the following: If A = {1,2}, then |p(p(A × p(A)))| = ?

A:

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: Suppose P(A) = 0.4 and P(B) and B, show that 0.1 ≤ P(An B) ≤ 0.4. = 0.7. With no other assumptions…

A: We have given thatP(A) = 0.4P(B) = 0.7We have to show that0.1 ≤ P(AB) ≤ 0.4

Q: If S= {a,b,c} with P(a)= 2P(b)= 4 P(c), find P(a)

A:

Q: α Let V₁ = {(₁)|a € R}. V₁ with standard V4 operations will fail both axiom "close under addition"…

A: Let A be a set and ∘ binary operation on A then 1. We say A is closed under the binary operation ∘…

Q: If P(n-1,3):P(n,4) = 1:9,Findn.

A:

Q: Let A = { {a}, {b}, {c}, {d}, {e} } Determine by extension P(A

A:

Q: Suppose that P(A) = 0.1, P(B) = 0.3, and P(A|B) + P(B|A) = 0.8. Find P(A ∩ B).

A: From the information, given thatThe formula of the conditional probability, for any two events…

Q: Compute x3 in two ways: by computing x, and x2, and by computing P³ [1] P= x₁ = 0.1 0.2 0.9 0.8 0.19…

A: Solution: The given matrix is, P=0.10.20.90.8,x0=10. Now compute x3 in two ways:

Q: Use Contrapositive method to proof the following statement. (a) Suppose a E Z, if a? + 5a is even,…

A: Given: using contrapositive method

Q: Let X N(10, 23). Then P( X< 10) =

A:

Q: -1 1 Let A= 1 Then, ||A||2 = -2 Select one: a. 9+V45 2 b. 8+V45 c. 10+V45 2 d. 7+V45

A:

Q: If P(A/B) = P(A) and P(B/A)=P(B), then A and B are: O A. Mutually exclusive O B. Dependent O C.…

A: Equally likely events:   The two events are said to be Equally likely event if every event has the…

Q: The weights of ice cream cartons are normally distributed with a mean weight of 11 ounces and a…

A: Given : μ=11 ounceσ=0.6 ounceX~N(μ=11,σ2=0.62)Let, for sample of size n,x¯~Nμx¯=μ,σx¯2=σn2

Q: Let det(A) = 5 and det(A + B) = 20. We conclude that det(/+A¬}B) = 15 O True False

A: Given det(A) = 5  det(A+B) = 20  Now by multiplying det(A-1) on both sides  (det(A-1)) (det(A+B)) =…

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

A: Ans#- Given, P(A | B) = 0, and P(A) = 0.15.            Are A and B        (a) Independent?…

Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

A: Given that

Q: Let B = -3 {CHEMED} 0 Find [x]s 3 3 and x = -8 23

A:

Q: 1 If the N(A) consists of all multiples of x = , then the rank of A 4 is: а. 3 O b. 2 O C. 4 O d. 1…

A: It is clear that from N(A)

Q: If x is N(0,2) find (a) P{1£x£2} and (b) P{1£x£2x³1}

A: Given that,  X~ N(0,2)  Where, mean of x= 0  Standard deviation of x= 2 We know that, z-score=…

Q: (b) If r23= 1, prove that R² (23) = 112=113 and 01.23 = 01 (1-12).

A:

Q: Suppose that P ( A ) = 0.4,  P ( B ) = 0.5 and A , B are disjoint. Compute P ( A c ∪ B c ) .

A: From the provided information, P (A) = 0.4, P (B) = 0.5 The events A and B are disjoint.

Q: Assume that P ( A ) = P ( B ). Show that A = B

A: If possible let A≠B and there is an element x ∈ A and x ∉ B Then {x} ∈ P(A) , but {x} ∉ P(B)

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.