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 <= x

Determine 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)

a)

And we can find this using the cumulative distribution function:

b)

And we can find this using the cumulative distribution function and the complement rule on this way:

c)

And we can find this using the cumulative distribution function:

d)

And we can find this using the cumulative distribution function and the complement rule on this way:

e)

And we can find this using the cumulative distribution function:

Step-by-step explanation:

For this case we have the following cumulative distribution function:

Part a

We want this probability:

And we can find this using the cumulative distribution function:

Part b

We want this probability:

And we can find this using the cumulative distribution function and the complement rule on this way:

Part c

We want this probability:

And we can find this using the cumulative distribution function:

Part d

We want this probability:

And we can find this using the cumulative distribution function and the complement rule on this way:

Part e

We want this probability:

And we can find this using the cumulative distribution function:

what i would say the best answer is a. 40.5