Final answer:
Without the specific values for the number of trials and the probability of success from the binomial PMF, it is not possible to calculate the standard deviation for the random variable X.
Step-by-step explanation:
To find the standard deviation of the binomial random variable X, we need to identify the number of trials (n) and the probability of success (p). The given binomial probability mass function (PMF) is not typical as it appears to contain a typo. However, from the context, we assume that X follows a binomial distribution with parameters n and p, which is expressed as X~B(n, p). in a binomial distribution, the mean (μ) is calculated as n*p and the variance (σ²) as n*p*(1-p). The standard deviation is the square root of the variance, σ = √(n*p*(1-p)). Without the specific values for n and p from the PMF, we cannot provide a numerical answer for the standard deviation.
If we had the correct binomial PMF Pₓ(x) = ℌ(n, x) * p^x * (1-p)^(n-x), where ℌ(n, x) represents the binomial coefficient, we could substitute n and p into the variance formula to calculate the standard deviation.