The random variable X takes on the values 1, 2 (or) 3 with probabilities $$rac{{2 + 5{ ext{P}}}}{5},rac{{1 + 3{ ext{P}}}}{5}$$ and $$rac{{1.5 + 2{ ext{P}}}}{5}$$ respectively the values of P and E(X) are respectively.

The random variable X takes on the values 1, 2 (or) 3 with probabilities $$\frac{{2 + 5{\text{P}}}}{5},\frac{{1 + 3{\text{P}}}}{5}$$ and $$\frac{{1.5 + 2{\text{P}}}}{5}$$ respectively the values of P and E(X) are respectively.

For calculating posterior probabilities (conditional probabilities under statistical dependence), the following information is available a) conditional probabilities b) original probability estimates (prior probabilities) of mutually exclusive and collectively exhaustive events c) Arbitrary event with probability

A

a) → b) → d) → c)

B

c) → b) → a) → d)

C

b) → c) → d) → a)

D

b) → a) → d) → c)

What is linear_congruential_engine? for some w using Mersenne Twister algorithm b) Pseudo-random number engine that generates random unsigned integers c) Pseudo-random number engine that generates random unsigned integers in the range for some w using lagged Fibonacci generator d) Pseudo-random number engine that generates random signed integers in the range for some w using Mersenne Twister algorithm

A

Pseudo-random number engine that generates random unsigned integers in the range for some w using Mersenne Twister algorithm

B

0, 2w-1

C

0, 2w-1

D

0, 2w-1

Consider the following statements: 1. A continuous random variable can take all values in an interval. 2. A random variable which takes a finite number of values is necessarily discrete. 3. Construction of a frequency distribution is based on data which are discrete. Which of the above statements are correct?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

Which of the following is a table with all possible values of a random variable and its corresponding probabilities?

A

Probability Density Function

B

Probability Mass Function

C

Probability Distribution

D

Cumulative distribution function

d/dx{tan-1(⃗ex x-1)+tan-1(e-x x²)} -এর সমান কোনটি?

A

0

B

ex

C

1

D

x²e-x

Suppose we have a random variable X where for the values k = 0, ..., 10, the associated probabilities are . What is the mean of X?

A

0.37

B

0.63

C

3.7

D

6.3

A joint sample space for two random variable X and Y has four elements (1,1), (2,2), (3,3) and (4,4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively. What is the probability of the event that X is less than three?

A

0.45

B

0.50

C

0.55

D

0.60

Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.

A

Both statements are correct

B

Both statements are incorrect

C

Statement I is correct while Statement II is incorrect

D

Statement I is incorrect while Statement II is correct

Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. A bag contains some number of Diamond of 4 different colors (Red, Pink, blue and yellow). What is the total number of Diamond in the bag? I. If 5 Pink Diamond from the bag are replaced by Yellow Diamond, Then the ratio of probabilities of picking 2 yellow Diamond at a time to picking 3 Blue Diamond at a time becomes (1/116). II. The different between probabilities of picking 2 Red Diamonds at a time and probability of picking 2 Blue Diamonds at a time is (23/330). III. If a Diamond is picked from the bag, then there is 40% chance that it is a red Diamond. Probability of picking 2 Red Diamond from the bag is (26/165).

A

The data in only statement I and II together are sufficient to answer the question.

B

The data in only statement I and III together are sufficient to answer the question.

C

The data in only statement III alone is sufficient to answer the question.

D

The data in at least any two of the 3 statements is necessary to answer the question.

E

None of the above

If ‘X’ is a random variable, taking values ‘x’, probability of success and failure being ‘p’ and ‘q’ respectively and ‘n’ trials being conducted, then what is the probability that ‘X’ takes values ‘x’? Use Binomial Distribution

A

P(X = x) = nCx px qx

B

P(X = x) = nCx px q(n-x)

C

P(X = x) = xCn qx p(n-x)

D

P(x = x) = xCn pn qx

The random variable X takes on the values 1, 2 (or) 3 with probabilities $$\frac{{2 + 5{\text{P}}}}{5},\frac{{1 + 3{\text{P}}}}{5}$$ and $$\frac{{1.5 + 2{\text{P}}}}{5}$$ respectively the values of P and E(X) are respectively.

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