SOLUTION: Problem 2 (13%)
Consider the random variable X and its probability mass function:
𝑋: 70 80 90
𝑃(𝑋 = 𝑥): 0.3 0.45 0.25
a- Find the expected value of this random
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-> SOLUTION: Problem 2 (13%)
Consider the random variable X and its probability mass function:
𝑋: 70 80 90
𝑃(𝑋 = 𝑥): 0.3 0.45 0.25
a- Find the expected value of this random
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Question 1182767: Problem 2 (13%)
Consider the random variable X and its probability mass function:
𝑋: 70 80 90
𝑃(𝑋 = 𝑥): 0.3 0.45 0.25
a- Find the expected value of this random variable.
b- Find the cumulative distribution of this random.
c- Calculate P(𝑋 ≥ 80) in two methods: Use the cumulative distribution and the probability mass function. Answer by math_tutor2020(3817) (Show Source):
Let's define a function C(X) such that it computes the cumulative probability up to and including that X value.
We'll define C(X) like so
C(70) = P(70) = 0.3
C(80) = P(70)+P(80) = 0.3+0.45 = 0.75
C(90) = P(70)+P(80)+P(90) = 0.3+0.45+0.25 = 1
So again, we define where k is a value in the domain of X.
We see that the probability of getting 80 or higher, based on that table above, is 0.45+0.25 = 0.70
Simply add the probability values for X = 80 or larger.
There's a 70% chance of this happening.
Or, we could note that C(70) = 0.30
From this, we could then say
P(𝑋 ≥ 80) = 1 - C(70)
P(𝑋 ≥ 80) = 1 - 0.30
P(𝑋 ≥ 80) = 0.70
This works because
P(70) + P(80) + P(90) = 1
The "P(80) + P(90)" portion is what we want while C(70) represents P(70)
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