An unfair coin with Pr[H]=0.25 is flipped 95 times. A random variable X is defined as the number of heads that occur. Find the standard deviation.
Any help??
To find the standard deviation of a binomial random variable, you can use the following formula:
σ = √[n * p * (1 - p)]
where σ is the standard deviation, n is the number of trials, and p is the probability of success.
In this case, the unfair coin has a probability of heads (success) of p = 0.25, and it is flipped 95 times (n = 95). Plug these values into the formula:
σ = √[95 * 0.25 * (1 - 0.25)]
Simplify the equation:
σ = √[95 * 0.25 * 0.75]
σ = √[17.8125]
Calculate the square root:
σ ≈ 4.217
Therefore, the standard deviation is approximately 4.217.