taufajane3887
15.02.2021 •
Mathematics
Suppose X is a normally distributed random variable with mean 0 and variance 1 (i.e., standard normal).
Compute the following (Hint: you can use the R functions pnorm and qnorm to answer these questions).
P r(X < 1:96)
P r(X > 1:64)
P r(0:5 < X < 0:5) 1% quantile, q:01 and 99% quantile, q:99 ? 5% quantile, q:05 and 95% quantile,
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Ответ:
Step-by-step explanation:
Given
--- Mean
--- Variance
Calculate the standard deviation
Solving (a): P(X < 1.96)
First, we calculate the z score using:
This gives:
The probability is then solved using:
From the standard normal distribution table
So:
Solving (b): P(X > 1.64)
First, we calculate the z score using:
This gives:
The probability is then solved using:
From the standard normal distribution table
So:
Solving (c): P(0.5 < X < 0.5)
This can be split as:
In probability:
becomes
Ответ:
answer:
d
step-by-step explanation: