List of top Mathematics Questions on Probability asked in TS PGECET

If \(A\) and \(B\) are independent random variables, then which of the following is correct?

Two dice are thrown simultaneously. Let $X$ be the random variable representing the absolute difference of the numbers appeared on the dice. The mean of $X$ is:

If $f(x)$ is the probability density function of an exponential distribution and $\frac{1}{\lambda}$ is its mean, then $\int_0^\infty x^2 f(x) \, dx =$}

Which of the following is not the property of a distribution function \( F(x) \) of a random variable \( X \)?

If $f(x)$ is the probability density function of an exponential distribution and $\frac{1}{\lambda}$ is its mean, then $\int_0^\infty x^2 f(x) \, dx =$}

Two dice are thrown simultaneously. Let $X$ be the random variable representing the absolute difference of the numbers appeared on the dice. The mean of $X$ is:

Which of the following is not the property of a distribution function \( F(x) \) of a random variable \( X \)?

Choose a possible probability density function from the given functions:

The probability density function of a continuous random variable is \[ f(x)= \begin{cases} \dfrac35 e^{-3x/5}, & x>0 \\ 0, & x\le0 \end{cases} \] The mean of the distribution is

If \(Z\) is a standard normal variable, \[ P(Z>z_1)=\alpha, \] \[ P(Z<z_2)=\beta \] and \(z_2<z_1\), then a possible value of \[ P(z_2<Z<z_1) \] is