23MA2001 Probability and Statistics MCQ

If two events A and B are independent and P(A) = 1/3, P(B) = 1/6, then find P(AՈB).

• 1/12
• 1/4
• 1/9
• 1/18

If P(A)=0.3,P(B)=0.6 and P(AՈB)=0.2 then find 𝑃( ̅A ∩ ̅𝐵 ).

• 0.3
• 0.5
• 0.4
• 0.1

A continuous random variable X has the probability density function f(x)=k(x)^2 0<x<2. Find

the value of k .

• 3/8
• 2/3
• 5/8
• 1/4

If F(x,y) is the cumulative distribution function of (X,Y) then F(-∞,y)=

• 0.5
• -1
• 1
• 0

An AI model for sentiment analysis correctly identifies the sentiment of tweets with an accuracy of 90%. If 50 tweets are analyzed, then find the expected number of correctly classified tweets.

• 30
• 40
• 50
• 45

The response time of a search engine follows an exponential distribution with a mean

of 0.8 seconds. Construct the pdf of exponential distribution.

• f(x) = 1.5 * e^(-1.5x) for x >= 0
• f(x) = 1.25 * e^(-1.25x) for x >= 0
• f(x) = 1.0 * e^(-1.0x) for x >= 0
• f(x) = 0.8 * e^(-0.8x) for x >= 0

A data scientist builds a multiple regression model for predicting server load (Y) using CPU usage (X₁), memory utilization (X₂), and number of users (X₃): Y = 1.25X₁ + 0.45X₂ + 0.02X₃ + 10.8. Predict the server load when X₁ = 60, X₂ = 70, and X₃ = 200.

• 121.3
• 98.7
• 130.2
• 115.5

Find the correlation coefficient between the size of the CPU cache (in mb) and the

time taken to execute a particular algorithm or program (in seconds), given that the regression coefficients are 0.4 and 0.9.

• 1.0
• 0.8
• 0.2
• 0.6

The critical value of Z for a one-tailed test at a 1% level of significance is _____.

• 2.33
• 3.00
• 2.58
• 1.96

What is Type II error?

• Type II error is the failure to accept a false null hypothesis.
• Type II error is the failure to reject a false null hypothesis.
• Type II error is the rejection of a true null hypothesis.
• Type II error is the acceptance of a true null hypothesis.