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)

Question

02-03-2020
Mathematics

contestada

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)

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dfbustos dfbustos · Answer 1 · 2020-03-03T13:52:13+01:00

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 a

We 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 b

We 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 c

We 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 d

We 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 e

We 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]