random-variable

The probability density function $f(x)$ of a random variable $X$ which takes real values is $$ f(x)=\frac{1}{3 \sqrt{2 \pi}} \exp \left(-\frac{x^2}{18}\right), x \in(-\infty,+\inft...

For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of...

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component...

For any discrete random variable X, with probability mass function P(X = j) = pj, Pj ≥ 0, j∈ {0,...,N}, and $\sum_{j=0}^{N} p_j = 1$, define the polynomial function $g_x(z) = \sum_...

If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X + 2)^2] equals _________.

Let $$X$$ be a Gaussian random variable with mean $$0$$ and variance $${\sigma ^2}$$ . Let $$Y=max(X,0)$$ where $$max(a, b)$$ is the maximum of $$a$$ and $$b$$. The median of $$Y$$...

Consider a random variable X that takes values + 1 and-1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = - 1 and + 1 are

If the difference between the expectation of the square of a random variable $$\left( {E\left[ {{X^2}} \right]} \right)$$ and the square of the expectation of the random variable $...

Let X be a random variable following normal distribution with mean + 1 and variance 4. Let Y be another normal variable with mean - 1 and variance unknown. If $$P\,(X\, \le \, - 1)...

Suppose that the expectation of a random variable X is 5. Which of the following statements is true?

Suppose that the expectation of a random variable X is 5. Which of the following statements is true?