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 on A

Q: Given X~ N(20,16), find c. P( 19 < X<23) (4 decimal place)

A: X~N(20,16) Mean(μ)=20 Variance(σ2)=16 standard deviation(σ)=16=4

Q: Suppose X ~ t5, calculate P[–1.476 ≤ X ≤ 3.365]

A: Given that random variable X follows t distribution with degrees of freedom 5

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that.   X~N( μ , ?^2 )   μ=5 , ? =1   Z-score =( x - μ )/?

Q: Q2. | For what values of a, b and c does the function 6, x = 0 f(x) = {2x2 + a, bx + c, 0 <x < 2 2…

A:

Q: A branch of a certain bank in New York City has six ATMs. Let X represent the number of machines in…

A: The cumulative distribution function of a random variable X can be defined as, ,  where, is…

Q: Let X~N(10,9).

A: The mean of the distribution is 10. The standard deviation of the distribution is 9.

Q: what is the t test for the above

A: A t-test is not appropriate for testing the hypothesis of equal proportions among three independent…

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

A:

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Question 5. Consider the following three statements about a real number x: • P(x): -1 ≤ x ≤ 3. •…

A: P(x) : -1≤x≤3 Q(x) : x2 &gt; x  x2 &gt; xx2 - x &gt; 0x(x-1) &gt; 0x &gt; 0 and x - 1 &gt;0 ⇒ x &gt;…

Q: 2. Suppose Y is G-measurable. Prove that Var(Y/G) = 0. %3D

A: Given that Y is G-measurable.

Q: @ Fs{f"cx>}=V Pf 66)-P Fs {f cx)} | proof: H.w.

A:

Q: A. If X~N(196,20), find x such that Pr(X < x) = 0.945.

A:

Q: Calculate the set op Convergence X72

A:

Q: a. What is p(t)=  b.By using the function from part a, what is the answer in integer ?

A:

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

A:

Q: 6. If X is t-distributed, show that X² is F-distributed.

A:

Q: 1. Let a be a positive real number and n be a natural number. Define S = {x €R: x >0 and x" a?…

A:

Q: uppose that S is the set of successful students in a classroom, and that F stands for the set of…

A: Given that expression we have to find the value of

Q: Let a1, a2, ...,a, be real numbers that are all contained in the interval [-7/2, 7/2]. Use the…

A:

Q: Suppose that Pr[A|B] = 1/3, Pr[A] = 1/6, and Pr[B Compliment] = 3/4. Find Pr[B|A Compliment]. (Hint:…

A: Given that, Suppose that P [A|B] = 1/3, P [A] = 1/6, and P [B Compliment] = 3/4.…

Q: Let s = {x €N : 2 < x < 9} and T = {x eN : 5 s x < 14}. Then snT = {x €N : 5s x < 9}. Select one: O…

A: We have to choose the correct option.

Q: (h) P(1.26 ≤ Z ≤ 2.50) (1) P(1.90 ≤ Z) (1) P(|Z| ≤ 2.50)

A: It is given that the standard normal random variable Z with mean 0 and variance 1.   Note: The…

Q: 6.3.6 For each real number x, let Ay = {3, –2} U {y E R : y > x}. Find U Ax and N Ax. xER xER

A:

Q: 2. Let f be the arithmetic function defined by f(n) = (-1)". Compute Z;(2) = f(n) n2 n=1 Hint:…

A: Solution: We will use the following formula Here n0=2

Q: 1. Consider the following intervals on R: A = (0,1); B = (1,2); and C = [2,3). For each pair of…

A:

Q: Suppose that all the people in a country are ranked according to their incomes, starting at the…

A:

Q: Show that Let ECR" is measurable set. If µ(E) >0, then E have a non-measurable subset

A: Here, we introduce the notation Gr :=G∩[0, r) + 1-r ∪ G∩[r,1) - r for G⊂[0,1) and r∈R. Note that…

Q: Give the value of c in the interval [-1, 2] that satisfies the conclusion of the mean value theorem…

A:

Q: let XnN(20, 0136) iF P(X<M) = 0.05 then the value of mis

A:

Q: if p is a prime, what is 10/p as a function of p?

A: We have to tell  What is 10/p as a function of p   It is given that p is prime

Q: Suppose P(E) =0.30, P(F) =0.34, and P(F ∩ E) =0.07. What is P(Ec | F)? (Enter answer as a decimal…

A: P(E) =0.30 P(F) =0.34P(F ∩ E) =0.07.

Q: c) Find the are under the curve on the interval -2 ≤x≤2

A: Given that , y=x2+2x

Q: Define f: N→ N by f(n) = 2". Find range(f).

A: