X is uniform on [0, 10]. Find P(2 < X < 5). Give a decimal.

f(x) = kx on [0, 5] and 0 elsewhere is a density. Which value of k makes it valid?

• 0.2
• 0.4
• 0.08
• 0.5

X is uniform on [0, 4], so its density is 1/4 there and 0 elsewhere. Which check confirms it is valid?

• The curve never dips below zero and the total area equals 1
• The curve reaches density height 1 at every point between 0 and 4
• The width 4 and height 1/4 give a rectangle whose total area is 0

Mia says P(X = 2) = 1/4 for X uniform on [0, 4], because f(2) = 1/4.

For a continuous variable, P(X = 5) = 0. Which conclusion about this fact is wrong?

• An interval around 5 can still have positive chance
• The value 5 is impossible and can never occur
• The density height at 5 can still be positive

Which function could be a density on [0, 1]?

• f(x) = 2x
• f(x) = x
• f(x) = 1 - 2x
• f(x) = 3x

A variable has cumulative function F(x) = x squared over 9 on [0, 3]. What is its density f(x) there?

• x over 9
• 2x over 9
• x squared over 3
• 2 over 9

The density f(x) = x over 8 on [0, 4] is valid. Find P(X < 2). Give your answer as a decimal.

Tom computes P(1 < X < 3) for uniform [0, 4] as f(2) = 1/4. What is wrong?

• He used the height at a point instead of the area
• He used endpoints 1 and 3 instead of endpoints 0 and 4
• He should have divided height 1/4 by interval width 2

A bus wait X is uniform on [0, 20] minutes. Use the complement of waiting at most 15 minutes to find P(X > 15). Give a decimal.