A continuous random variable X has a probability density f(x) = e<sup>-x</sup>, 0 1} is

An object X sinks in liquids P and Q but floats in liquid R. Which of the following conclusions can be made from these observations? A) Density of X is more than the density of P B) Density of X is less than the density of R C) Density of P is equal to the density of R D) Density of P is less than the density of R

A

A, B, C

B

A, B, D

C

B, C, D

D

A, C, D

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

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

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

If {x} is a continuous, real valued random variable defined over the interval (-$$\infty $$, +$$\infty $$) and its occurrence is defined by the density function given as:
$${\text{f}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}$$ where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$

A

1

B

0.5

C

$$\pi $$

D

$$\frac{\pi }{2}$$

Let f(x) be the continuous probability density function of a random variable X. The probability that a

A

$${\text{f}}\left( {{\text{b}} - {\text{a}}} \right)$$

B

$${\text{f}}\left( {\text{b}} \right) - {\text{f}}\left( {\text{a}} \right)$$

C

$$\int\limits_{\text{a}}^{\text{b}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$

D

$$\int\limits_{\text{a}}^{\text{b}} {{\text{xf}}\left( {\text{x}} \right){\text{dx}}} $$

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

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.

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

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

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

A continuous random variable X has a probability density function f(x) = e^-x, 0 1} is

A

0.368

B

0.5

C

0.632

D

1.0

A continuous random variable X has a probability density f(x) = e^-x, 0 1} is

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A continuous random variable X has a probability density f(x) = e-x, 0 1} is

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A continuous random variable X has a probability density f(x) = e^-x, 0 1} is