Errors in an experimental transmission channel are found when thetransmission is checked by a certifier that detects missing pulses.The number of errors found in a eight-bit byte is a random variablewith the following distribution:F(x) = { 0 x<1 0.7 1 <= x < 4 0.9 4 <= x < 7 1 7 <= xDetermine each of the following probabilities:(a) P(X <= 4) (b) P(X > 7)(c) P(X <= 5) (d) P(X > 4)(e) P(X <= 2)

Answer:a) [tex] P(X \leq 4)[/tex]And we can find this using the cumulative distribution function:[tex] P(X \leq 4) = F(4) = 0.9[/tex]b) [tex] P(X > 7)[/tex]And we can find this using the cumulative distribution function and the complement rule on this way:[tex] P(X >7) =1-P(X\leq 7)= 1- F(7) = 1-1 = 0[/tex]c) [tex] P(X \leq 5)[/tex]And we can find this using the cumulative distribution function:[tex] P(X \leq 5) = F(5) = 0.9[/tex]d) [tex] P(X > 4)[/tex]And we can find this using the cumulative distribution function and the complement rule on this way:[tex] P(X >4) =1-P(X\leq 4)= 1- F(4) = 1-0.9 = 0.1[/tex]e) [tex] P(X \leq 2)[/tex]And we can find this using the cumulative distribution function:[tex] P(X \leq 2) = F(2) = 0.7[/tex]Step-by-step explanation:For this case we have the following cumulative distribution function:[tex] F(x) = 0 , x<1[/tex][tex] F(x) = 0.7, 1 \leq x <4[/tex][tex] F(x) = 0.9, 4 \leq x <7[/tex][tex] F(x) = 1, x \geq 7[/tex]Part aWe want this probability:[tex] P(X \leq 4)[/tex]And we can find this using the cumulative distribution function:[tex] P(X \leq 4) = F(4) = 0.9[/tex]Part bWe want this probability:[tex] P(X > 7)[/tex]And we can find this using the cumulative distribution function and the complement rule on this way:[tex] P(X >7) =1-P(X\leq 7)= 1- F(7) = 1-1 = 0[/tex]Part cWe want this probability:[tex] P(X \leq 5)[/tex]And we can find this using the cumulative distribution function:[tex] P(X \leq 5) = F(5) = 0.9[/tex]Part dWe want this probability:[tex] P(X > 4)[/tex]And we can find this using the cumulative distribution function and the complement rule on this way:[tex] P(X >4) =1-P(X\leq 4)= 1- F(4) = 1-0.9 = 0.1[/tex]Part eWe want this probability:[tex] P(X \leq 2)[/tex]And we can find this using the cumulative distribution function:[tex] P(X \leq 2) = F(2) = 0.7[/tex]