Probability

Let X be a random variable, and let P(X=x) denote the probability that X takes the value x. Suppose that the points (x,P(X=x)),x=0,1,2,3,4, lie on a fixed straight line in the xy-plane, and P(X=x)=0 for all x∈ℝ− {0,1,2,3,4}. If the mean of X is ‌

5

2

, and the variance of X is α, then the value of 24α is _____.