Question

random variable X has this probability distribution:

x 0 1 2 3 4 5

P(X=x) 0.1 0.2 0.05 0.1 ? 0.3

Find f(4)

Answer 1

The sum of all probabilities for different values of $x$ must be equal to $1.$ We receive: $\sum_{x=0}^5P(X=x)=1$. From the latter we get: $0.1+0.2+0.05+0.1+0.3+P(X=4)=1$. We receive: $0.75+P(X=4)=1;$ $P(X=4)=0.25$. In case we denote: $f(x)=P(X=x)$, we get: $f(4)=P(X=4)=0.25.$