List of top Questions asked in GATE AG

In a locality 'A', the probability of a convective storm event is 0.7 with a density function \[ f_{X_1}(x_1) = e^{-x_1}, \; x_1 > 0 \] The probability of a tropical cyclone-induced storm in the same location is given by the density function \[ f_{X_2}(x_2) = 2 e^{-2x_2}, \; x_2 > 0 \] The probability of occurring more than 1 unit of storm event is \underline{\hspace{3cm}} (rounded off to 2 decimal places).

The probability that a storm event with a return period of 20 years will occur once in a 5-year period is \underline{\hspace{6cm}} (rounded off to 2 decimal places).

The probability of having 53 Sundays in a randomly selected leap year is __________.

Let $X$ be a continuous random variable denoting the temperature measured. The range of temperature is $[0, 100]$ degree Celsius and the probability density function of $X$ be $f(x) = 0.01$ for $0 \le X \le 100$. The mean of $X$ is \(\underline{\hspace{2cm}}\)