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

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: Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000…

A: Table :

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: 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: Find numbers m and M Such that m<f'(1)< M figure in (1.4,1.3) l1,2 (1.6, 1,4) +

A: Given: The graph of f as  To find: The numbers m and M such that m&lt;f'1&lt;M

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

A:

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

A:

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

A: