Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at X = -1 and +1 are

A probability distribution with right skew is shown in the figure.
Probability and Statistics mcq question image

The correct statement for the probability distribution is

A

Mean is equal to mode

B

Mean is greater than median but less than mode

C

Mean is greater than median and mode

D

Mode is greater than median

The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is

A

0.25

B

0.33

C

0.50

D

0

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

Arrange the following steps in sequence in order to calculate the probability of an event through Naïve Bayes classifier. I. Find the likelihood probability with each attribute for each class. II. Calculate the prior probability for given class labels. III. Put these values in Bayes formula and calculate posterior probability. IV. See which class has a higher probability, given the input belongs to the higher probability class.

A

I → II → III → IV

B

II → I → III → IV

C

III → II → I → IV

D

II → III → I → IV

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

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

A random variable X has an exponential distribution with probability distribution function is given by f(x)= 3e-3x for x>0 = 0 otherwise Find probability that X is not less than 2.

A

e-3

B

e-6 – 3

C

e-6

D

e-6 – 1

Consider the continuous random variable with probability density function
f(t) = 1 + t for -1 ≤ t ≤ 0
= 1 - t for 0 ≤ t ≤ 1
The standard deviation of the random variable is

A

$$\frac{1}{{\sqrt 3 }}$$

B

$$\frac{1}{{\sqrt 6 }}$$

C

$$\frac{1}{3}$$

D

$$\frac{1}{6}$$

Consider a Gaussian distributed random variable with zero mean and standard deviation σ. The value of its cumulative distribution function at the origin will be

A

0

B

0.5

C

1

D

10 σ

Probability plots are graph of ranked data plotted against the cumulative frequency, with a vertical scale chosen so that the cumulative distribution of assumed type is a _________

A

Parabola

B

Straight line

C

Hyperbola

D

Pulse

Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at X = -1 and +1 are

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