Expectation, Variance, Covariance and Correlation Previous Year Questions (PYQs) for GATE DA: 3+ Solved Questions with Step-by-Step Solutions

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:

Let $X$ and $Y$ be two independent random variables. $X$ follows $Bernoulli(p=0.3)$ distribution and $Y$ follows $Normal(\mu =0,{\sigma }^2=100)$ distribution.

Which of the following options is the variance of $(2X-1)Y$?

Two fair coins are tossed independently. X is a random variable that takes a value
of 1 if both tosses are heads and 0 otherwise. Y is a random variable that takes a
value of 1 if at least one of the tosses is heads and 0 otherwise.
The value of the covariance of X and Y is ______ (rounded off to three decimal
places).