Let \( X \) and \( Y \) be discrete random variables with joint probability mass function \[ p_{X, Y}(m, n) = \frac{\lambda^n e^{-\lambda} 2^n m! (n - m)!}{n!}, \quad m = 0, \dots, n, \quad n = 0, 1, 2, \dots, \] where \( \lambda \) is a fixed positive real number. Then which one of the following options is correct?
The range of the real valued function \( f(x) =\) \(\sin^{-1} \left( \frac{1 + x^2}{2x} \right)\) \(+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)\) is:
The value of shunt resistance that allows only 10% of the main current through the galvanometer of resistance \( 99 \Omega \) is: