Suppose X and Y are random variables. The conditional expectation of X given Y is denoted by EX|Y. ThenEEX|Yequals
Let X be a continuous random variable whose cumulative distribution function (CDF) FX(x), for some t, is given as follows: FX(x)=0xtxt4ttx41x4 If the median of X is 3, then what is the value of t?
Let X = aZ + b, where Z is a standard normal random variable, and a, b are two unknown constants. It is given that E[X] = 1, E[(X E[X])Z] = 2, E[(X E[X])2 ] = 4, where E[X] denotes the expectation of random variable X. The values of a, b are:
It is given that P(X 2) = 0.25 for an exponentially distributed random variable X with E[X]=1, where E[X] denotes the expectation of X. What is the value of ? (ln denotes natural logarithm)