List of top Statistics Questions asked in GATE Statistics

Let \( X \) be a random variable having the Poisson distribution with mean \( \log_e 2 \). Then \( E\left( e^{(\log_e 3)X} \right) \) equals:
Let \( X_1, \dots, X_n \) be a random sample from a uniform distribution over the interval \( \left( -\frac{\theta}{2}, \frac{\theta}{2} \right) \), where \( \theta>0 \) is an unknown parameter. Then which of the following options is/are correct?