Chi-Squared Distribution Variance Calculation
The variance of a chi-squared ($\chi^2$) distribution is determined by its degrees of freedom ($k$). The formula for the variance is:
$ \text{Variance} = 2k $
Applying the Variance Formula
In this question, the degrees of freedom ($k$) for the $\chi^2$ distribution is given as 10.
Substitute $k=10$ into the variance formula:
$ \text{Variance} = 2 \times 10 $
$ \text{Variance} = 20 $
Therefore, the variance of a $\chi^2$ distribution with 10 degrees of freedom is 20.
Important Questions from Continuous Distributions
Probability density function of a random variable X is given below
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0.25}&{if\;1 \le x \le 5}\\ 0&{otherwise} \end{array}} \right.\)
P (X ≤ 4) is
The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is _________
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs 500 is _______
The number of parameters in the univariate exponential and Gaussian distributions, respectively are
Find the value of λ such that the function f (x) is a valid probability density function. _______
\(f\left( x \right)\begin{array}{*{20}{c}} { = \lambda \left( {x - 1} \right)\left( {2 - x} \right)}&{for1 \le x \le 2}\\ { = 0}&{otherwise} \end{array}\)
