statistics

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20. Ignoring permutations, the number of...

Suppose a random variable Z follows Normal($\mu$ = 0, $\sigma^2$ = 1) distribution with probability density function $g(z)$ and cumulative distribution function $G(z)$. Another ran...

Let X_1,X_2,...,X_n be n independent random variables. Each of the random variables follows Normal(μ = 0, σ² = 1) distribution. Define X̄ = (1/n)Σ_{i=1}^n X_i . Which of the follow...

For a given data set {x1, x2, ..., xn}, where n = 100, it is known that $\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99$ Let us denote $\bar{x} = \frac{1}{n} \sum_...