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IB Mathematics: Applications and Interpretation HL · 13.2: Probability Distributions · 13.2.2

Name Date

Expected value of a discrete random variable Problem set B

Show the sum for E(X) each time. Give decimals exactly or to 3 significant figures. Check that each table adds to 1.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. The table shows the probability distribution of X, the number of pets in a household.

    x01234P(X = x)0.220.310.270.120.08
    1. (a) Find E(X).
    2. (b) Can X take the value E(X)? Explain.

  2. A quiz round awards Z points. The table shows the probability distribution of Z. Find E(Z).

    z5102550P(Z = z)0.450.300.200.05

  3. The random variable Y has distribution \(P(Y=y)=0.02(y^2-10y+24)\) for y = 0, 1, 2, 3.

    1. (a) Write the probability distribution of Y as a table.
    2. (b) Find E(Y).

  4. The table shows the probability distribution of Y.

    y24710P(Y = y)0.060.04k2k
    1. (a) Find the value of k.
    2. (b) Find P(Y ≤ 7).
    3. (c) Find E(Y).

  5. The table shows the probability distribution of Z, where k is a constant.

    z3691215P(Z = z)0.08k0.223k0.3
    1. (a) Find the value of k.
    2. (b) Find P(Z ≤ 9).
    3. (c) Find P(Z > 6 | Z ≤ 12).

In context

  1. A shelf holds 6 hardback books and 3 paperback books. Two books are taken at random without replacement. X is the number of paperbacks taken.

    1. (a) Find the probability distribution of X.
    2. (b) Find E(X).

  2. A kiosk records X, the number of drinks a customer buys. The table shows its probability distribution.

    x0123P(X = x)0.200.400.300.10
    1. (a) Find E(X).
    2. (b) 150 customers are expected in a day. How many drinks should the shop expect to sell?

  3. The number of books, Y, borrowed by a student in a visit has distribution \(P(Y=y)=0.01(y^2-y+15)\) for y = 2, 3, 4, 5.

    1. (a) Write the probability distribution of Y as a table.
    2. (b) Find E(Y).

Stretch

  1. A box holds 9 fuses, 3 of them faulty. Three fuses are tested at random without replacement. X is the number of faulty fuses tested.

    1. (a) Find the probability distribution of X.
    2. (b) Find E(X).

  2. The table shows the probability distribution of Y, the number of points a player scores in a round.

    y12345P(Y = y)k0.12k0.20.1
    1. (a) Find the value of k.
    2. (b) Find E(Y).
    3. (c) Find P(Y > E(Y)).

jmaths.xyz · AI HL · 13.2.2 Expected value of a discrete random variable