According to the probability distribution represented by the histogram, the value of E(x) is 39/16
How to determine the value of P(X = 3)
For a probability distribution, we have:
[tex]\sum P(x)= 1[/tex]
This means that:
P(0) + P(1) + P(2) + P(3) +P(4) = 1
Using the values on the histogram, we have:
0 + 1/4 + 1/8 + P(3) + 1/16 = 1
Multiply through by 16
4 + 2 + 16P(3) + 1 = 16
Evaluate the like terms
16P(3) = 9
Divide both sides by 16
P(3) = 9/16
Hence, the value of P(X = 3) is 9/16
How to determine the value of P(X < 3)
This is calculated using:
P(X < 3) = P(0) + P(1) + P(2)
Using the values on the histogram, we have:
P(X < 3) = 0 + 1/4 + 1/8
Evaluate
P(X < 3) = 3/8
Hence, the value of P(X < 3) is 3/8
How to determine the value of P(1 ≤ X ≤ 4)
This is calculated using:
P(1 ≤ X ≤ 4) = P(1) + P(2) + P(3) + P(4)
Using the values on the histogram, we have:
P(1 ≤ X ≤ 4) = 1/4 + 1/8 + 9/16 + 1/16
Evaluate
P(1 ≤ X ≤ 4) = 16/16
Simplify
P(1 ≤ X ≤ 4) = 1
Hence, the value of P(1 ≤ X ≤ 4) is 1
How to determine the value of E(x)
This is calculated using:
[tex]E(x) = \sum x \times P(x)[/tex]
Using the values on the histogram, we have:
E(x) = 0 * 0 + 1 * 1/4 + 2 * 1/8 + 3 * 9/16 + 4 * 1/16
Evaluate
E(x) = 39/16
Hence, the value of E(x) is 39/16
Read more about probability distribution at:
https://brainly.com/question/24756209
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