3. Consider tw o evénts A and B such that Pr(A)= 1/3 and Pr(B)= 1,2. Determine the value of Pr(B 0A) for each of the following conditions: (a) A and B are disjoint3 (b) AC B: (c) Pr(A O B) =1/8.

Q: Let X - Geom(p). Let s 2 0 be an integer. Show that P(X > s) = (1 – p)s. (Hint: The probability that…

A: Geometric distribution In series of Bernoulli trials, the random variable X denotes number of trials…

Q: Events  A and B are disjoint. Pr[A] =0.25 and Pr[B] =0.35. Find Pr[A U B']

A: A and B are disjoint.  This means, that: PA∩B=0

Q: A random variable has a PDF f(x) = i) The value of C. ii) P (X> 2). √√25-x² -5<x<5. Find

A:

Q: In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a…

A: Given that,In PCA, we obtain z∈Rk from x∈Rn as follows:z=|u(1)| |u(2)| ...…

Q: find c if p(o<z<c)=.2123

A: Solution: Here, we need to find the value of c.

Q: On donne P(A) = 0,4 ; P(A N B) = (7 %3D %3D * =0,3 et P(AUB)=D0.8. P(B) 0.7 0.2 0.3

A: Given,     The objective is to find PB

Q: Q. 62 Give the formula for calculating statistic x² in case of contingency table of order (2 x 2).

A:

Q: (a) A B (b) (c) P(A)=0.82, P(AUB) = 0.91, P(B) = 0.64

A:

Q: Q8. Let m = 5k(728) and n = 5k(616) where k 2 0 then determine if %3D (a) t(m) = t(n) (b) o(m) =…

A: is a function that denotes the number of positive divisor of n is a multiplicative function. If…

Q: Cor. 2. For three non-mutually exclusive events A, B and C, we have P(AUBUC) = P(A) + P(B) + P(C) –…

A:

Q: Let P(t) = 28(1 - e-kt) + 57 represent the expected score for a student who studies t hours for a…

A: The function that represent the expected score for a student is given as P(t)=28(1-e-kt)+57

Q: Probability. Don't understand.

A: The objective of the question is to calculate the probabilities of certain events occurring when…

Q: Jim’s bookcase holds 4 geometry books, 1 calculus book, and 3 algebra books.  Books are taken at…

A: Total number of books in the bookcase is 8  (4 +3+1)   Number of books other day algebra book  is 5…

Q: Pr(A) = 0.2 %3D Pr(B) = 0.4 %3D Pr(A|B) = 0.5 Hence, find Pr(A n B) Select one: О 0.1 O 0.2 O 0.3 O…

A:

Q: If A = and B = and N(A) = N(B) then %3D O a a= 2 and 8= 4 O b. a = 4 and 8 = 2 Oc a=-4and 8 = 2 Od.…

A: We have to solve given problem:

Q: Consider a random poker hand of 5 cards. Let X be the number of Hearts in this hand, and let Y be…

A: There are  13 hears,  13 diamonds and  26 cards that are neither hearts or diamonds in a deck of 52…

Q: For events A and B, prove that P (An B) >1– P (Aº) – P (Bº).

A: We want to prove the above result. Result: 0≤P(A)≤1

Q: (a) Compute P(E' n F'). (b) Are E and F independent? (c) Are E and F mutually exclusive?

A: here p(E) = 0.3 p(F) = 0.6  p(E | F) = 1/6

Q: A student is taking the online homework which allows at most 10 attempts and keeps attempting until…

A: At most 10 attempts are allowed for a student who is taking the online homework and he keeps…

Q: State whether the standardized test statistic t indicates that you should reject the null…

A:

Q: 00 dt

A: ∫0∞ e-t2dt

Q: Show that 1 – R1.23 = (1 – r12²) (1 – r13,22 ) Deduce that (i) R, 23 2r,2, (ii) R? = r12² + r13², if…

A: Answer: For the given data,

Q: Let P(E)=0.85, P(F) = 0.23, and P(EUF) = 0.94. Find (a) P(EIF) and (b) P(FIE). (a) P(EIF) = (Type an…

A:

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: f(x) = D, = R/{1,–1} 3 %3D %3D :Select one True False

A: Given function f(x)=3x2+1

Q: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: State whether the standardized test statistic t indicates that you should reject the null…

A: We have given that  The critical value t0=1.974 And given test statistic t. NOTE:- According to…

Q: Let P(A) = 0.3 and P(AUB) = 0.7. For what value of P(B) are A and B independent? O4/7 1/4 O 1/3 O…

A: Given: P(A) = 0.3P(A ∪ B) = 0.7

Q: Using Eq. 8.1.2 together with the values of D, and D2, we can evaluate D, for // in principle any…

A: Since I have solved similar ones, Let us start finding the pattern.....     The values of D1, D2…

Q: Jordan is practicing field goals. On each attempt, he have a 0.35 chance of making it. Let X be the…

A: It is given that n=5 and p=0.35. (i) EX=n×p=5×0.35=1.75

Q: 0.1. Find P(E U F). 0.1 and P(F) The two events E and F are independent with P(E) = X

A: to work out the required probabilty

Q: J and K are independent events. P(JK) = 0.3. Find P(J).

A: Two events J and K are given.

Q: T1. Colors in print media, on computer monitors, and on televi- sion screens are implemented using…

A: The conversion from  model to the  is accomplished by the matrix We have to find the matrix used to…

Q: 14. For two events we have Pr[A]=.29, Pr[B]=.43, and Pr[AUB]=.65. Find Pr[ANB]. (a) .27 (b) .07 (c)…

A:

Q: Which of the following is a cube root of – 2.3 – j1.25 1.3782 + j3.3075 -1.3593 - jo.2276 -1.3782 -…

A:

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

Q: Find the value z associated P(|Z| < z) = 0.10.

A:

Q: for x >1 f(x) = otherwise Given that a randomly selected home is insured for at least 1.5, what is…

A:

Q: y 1 2 4 8 16 p(y) 0.05 0.10 0.35 0.40 0.10

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.