A discrete random variable X whose probability distribution function is \$P(X=x) = x/12\$
x ∈ {1, 2, 3, 4, 5} .Find P(X≤4).?

P(X≤4) = F(4)

P(X=x) = \$\sum_{i=1}^n x_ip_i\$

To find value of P(X≤4) = \$\sum_{i=1}^4 x_ip_i (or) x_1p_1 + x_2p_2 + x_3p_3 + x_4p_4\$

Taking the values till 4 as P(X≤4)

P(X=1) + P(X=2) +P(X=3) + P(X=4)

\$P(X=x) = x/12\$

Substitute x = {1, 2, 3, 4, 5}
\$P(X≤4)\$

\$1/12 + 2/12 + 3/12 + 4/12\$

P(X≤4)

\$(1+2+3+4)/12\$

Simplification

P(X≤4) = \$10/12\$

After simplification

P(X≤4) = 0.83

0 < \$p_i\$ < 1 Condition is satisfied

Answer

C