Errors in an experimental transmission channel are found when thetransmission is checked by a certifier that detects missing pulses.The numb

Question

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)

in progress 0
Arianna 2 months 2021-10-09T06:40:47+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-09T06:42:07+00:00

    Answer:

    a) P(X ≤ 4) = 0.9

    b) P(X>7) = 0

    c) P(X ≤ 5) = 0.9

    d) P(X>4) = 0.1

    e) P(X≤2)= 0.7

    Step-by-step explanation:

    Hello!

    Given the distribution of cumulative probability

            0        for  X < 1

    F(x)  0.7     for 1 ≤ X < 4

           0.9     for  4 ≤ X < 7

             1        for 7 ≤ X

    To determine each of the asked probabilities you have to select the probability corresponding to the defined intervals for X:

    a) P(X ≤ 4) = 0.9

    This value of X is included the interval “4 ≤ X < 7” so the corresponding probability is 0.9

    b) P(X>7) = 0

    This is equal to the expression:

    1 – P(X≤7)

    This expression is included in the last interval so the probability is 1

    1 – 1 = 0

    c) P(X ≤ 5) = 0.9

    5 is included in the third interval “4 ≤ X < 7” so the corresponding probability is 0.9

    d) P(X>4) = 0.1

    P(X>4) = 1 – P(X≤4)

    P(X≤4) is in the interval of definition “4 ≤ X < 7” so the corresponding probability is 0.9

    1 – 0.9 = 0.1

    e) P(X≤2)= 0.7

    The value X=2 is included in the second interval “for 1 ≤ X < 4”, so the probability is 0.7

    I hope it helps!

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )