The cumulative distribution function of x is 0.60.
Here X has discrete probability distribution.
[tex]$\begin{aligned}&\mathrm{P}(\mathrm{X}=1)=0.30 \\&P(X=3)=F(3)-F(1)=0.40-0.30=0.10 \\&P(X=4)=F(4)-F(3)=0.45-0.40=0.05 \\&P(X=6)=F(6)-F(4)=0.60-0.45=0.15 \\&P(X=12)=F(12)-F(6)=1-0.60=0.40\end{aligned}$[/tex]
Following table shows the pmf:
X P(X=x)
1 0.3
3 0.1
4 0.05
6 0.15
12 0.4
Following is the graph of CDF is [SEE in attachement]
[tex]$P(3 \leq X \leq 6)=F(6)-F(1)=0.60-0.30=0.30$P(X \geq 4)=1-F(3)=1-0.40=0.60$[/tex]
The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, evaluated at x. It is employed to describe a table's random variables' probability distribution.
To learn more about Cumulative Distribution Function visit:https://brainly.com/question/15353924
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