Probability & Statistics

Single correct

• A1/4
• B1/3
• C1/2
• D2/3

Numerical answer

Single correct

• A$X$ is an exponential random variable
• B$X$ is a normal random variable
• C$X$ is a Poisson random variable
• D$X$ is a uniform random variable

Numerical answer

Numerical answer

Numerical answer

Numerical answer

Numerical answer

Numerical answer

Single correct

• AThe events $X$ and $Y$ are mutually exclusive
• BThe events $X$ and $Y$ are independent
• CEither event $X$ or $Y$ must occur
• DEvent $X$ is more likely than event $Y$

One or more correct

• AThe two events $A$ and $B$ are independent
• B$P(A \cup B) = 0.7$
• C$P(A \cap B^c) = 0.2$, where $B^c$ is the complement of the event $B$
• D$P(A^c \cap B^c) = 0.4$, where $A^c$ and $B^c$ are the complements of the events $A$ and $B$, respectively

Numerical answer

Single correct

• A$\dfrac{1}{324}$
• B$\dfrac{5}{324}$
• C$\dfrac{7}{324}$
• D$\dfrac{11}{324}$

Single correct

• A$\bar{z} = \bar{x}\bar{y}$
• B$\bar{z} \le \bar{x}\bar{y}$
• C$\bar{z} \ge \bar{x}\bar{y}$
• D$\bar{z} \le \bar{x}$

One or more correct

• A$A$ and $B$ are independent.
• B$A$ and $C$ are independent.
• C$B$ and $C$ are independent.
• D$\text{Prob}(B \mid C) = \text{Prob}(B)$

Answer key coming soon

Numerical answer

Answer key coming soon

Single correct

• ABoth $S_1$ and $S_2$ are true.
• B$S_1$ is true, but $S_2$ is false.
• C$S_1$ is false, but $S_2$ is true.
• DBoth $S_1$ and $S_2$ are false.

Answer key coming soon

Numerical answer

Answer key coming soon

Numerical answer

Answer key coming soon

question   probability of answering correctly   marks
QuesA      0.8                                  10
QuesB      0.5                                  20

Single correct

• AFirst QuesA and then QuesB. Expected marks 14.
• BFirst QuesB and then QuesA. Expected marks 14.
• CFirst QuesB and then QuesA. Expected marks 22.
• DFirst QuesA and then QuesB. Expected marks 16.

Answer key coming soon