Mean and Percentiles for a Continuous Random Variable (VCE SSCE Mathematical Methods): Quizzes

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Mean and Percentiles for a Continuous Random Variable
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What does the mean of a continuous random variable represent?

Long-run average value expected

For continuous RV XX with pdf ff, what is the formula for E(X)E(X)?

E(X)=xf(x)dxE(X) = \int_{-\infty}^{\infty} x f(x) dx

Which Greek letter denotes the mean of a random variable?

μ\mu (mu)

What is the formula for E[g(X)]E[g(X)] where gg is a function?

g(x)f(x)dx\int_{-\infty}^{\infty} g(x)f(x) dx

For linear function with constants aa and bb, what is E(aX+b)E(aX + b)?

aE(X)+baE(X) + b

Generally, is E[g(X)]E[g(X)] equal to g[E(X)]g[E(X)]?

No, except for linear functions

What does a percentile value divide in a distribution?

% of values falling below it

What value of qq gives the 75th percentile?

q=0.75q = 0.75

What is the median of a continuous random variable?

The 50th percentile

For median mm, what is Pr(Xm)Pr(X \leq m)?

0.50.5

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