Suppose X and Y are random variables with E(X) = 37, var(X) = 5, E(Y) = 62, and var(Y) = 12. What are the expected value and variance of the random variable X + Y?

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

Suppose, it is calculated that 'a' is 4 and 'b' is 2 for a particular estimating line with one independent Variable. If the independent variable has a value of 5, what value should be expected for the dependent variable?

A

6

B

11

C

14

D

22

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

Suppose X and Y are random variables with ?x = 32, ?x = 5, ?y = 44, and ?y = 12. Given that X and Y are independent, what are the mean and standard deviation of the random variable X + Y?

A

?x+y = 76, ?x+y = 8.5

B

?x+y = 76, ?x+y = 13

C

?x+y = 76, ?x+y = 17

D

?x+y = 38, ?x+y = 17

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

A

0

B

ex

C

1

D

x²e-x

"BDL Ltd. is currently preparing its cash budget for the year to 31 March 20XX. An extract from its sales budget for the same year shows the following sales values.
Rs
March 60,000
April 70,000
May 55,000
June 65,000
40% of its sales are expected to be for cash. Of its credit sales, 70% are expected to pay in month after sale and take a 2% discount. 27% are expected to pay in the second month after the sale, and the remaining 3% are expected to be bad debts. The value of sales budget to be shown in the cash budget for May 20XX is"

A

Rs. 60,532

B

Rs. 61,120

C

Rs. 66,532

D

Rs. 86,620

Suppose, you got a situation where you find that your linear regression model is under fitting the data. In such situation which of the following options would you consider?
1. I will add more variables
2. I will start introducing polynomial degree variables
3. I will remove some variables

A

1 and 2

B

2 and 3

C

1 and 3

D

1, 2 and 3

Read the following sentences and choose the correct option. (i) Variables can only take discrete values while Attributes can take continuous values. (ii) Variables can only take continuous values while Attributes take discrete value. (iii) Attributes and variables are dependent on each other. (iv) Width of an impeller blade is a variable but no. of defective blades in a lot is an attribute.

A

(i) and (iii) are correct

B

(i)and (iii) are incorrect

C

Only (i) is correct

D

(i), (ii), (iii) and (iv)

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2) the standard deviation of Y is

A

3

B

2

C

√2

D

1

The random variable X is defined by the density f(x) = 0.5u(x) e(0.5x). What is the variance of the random variable x is?

A

1/10

B

3/80

C

5/16

D

3/16

Suppose X and Y are random variables with E(X) = 37, var(X) = 5, E(Y) = 62, and var(Y) = 12. What are the expected value and variance of the random variable X + Y?

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