A die is rolled 5 times. Getting an odd numbe | vedclass

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(D) The distribution of successes follows a binomial distribution with parameters $n$ and $p$.The variance of a binomial distribution is given by the

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$\frac{5}{4}$

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(D) The distribution of successes follows a binomial distribution with parameters $n$ and $p$.The variance of a binomial distribution is given by the formula $Var(X) = npq$,where $n$ is the number of trials,$p$ is the probability of success,and $q = 1 - p$ is the probability of failure.In a single roll of a die,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$. The odd numbers are $\{1, 3, 5\}$.Therefore,the probability of success $p = \frac{3}{6} = \frac{1}{2}$.The probability of failure $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.Given that the die is rolled $n = 5$ times.Substituting these values into the variance formula:$Var(X) = n 	imes p 	imes q = 5 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{5}{4}$.

$A$ die is rolled $5$ times. Getting an odd number in one trial is considered as a success. The variance of the distribution of successes is

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