Discrete Random Variables Homework

Solve these problems, then check your answers against the given solutions.

Solutions to Exercises

    1. $200,000;$600,000;$400,000
    2. third investment
    3. first investment
    4. second investment

    1. 0.2
    2. 2.35
    3. 2-3 children

    1. X = the numbeof dice that show a 1
    2. 0,1,2,3,4,5,6
    3. X-B (6, 1/6)
    4. 1
    5. 0.00002
    6. 3 dice

    1. X = the number of students that will attend Tet.
    2. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
    3. X-B(12,0.18)
    4. 2.16
    5. 0.9511
    6. 0.3702

    1. X = the number of fortune cookies that have an extra fortune
    2. 0,1,2,3,... 144
    3. X-B(25,0.40) or P(4.32)
    4. 4.32
    5. 0.0124 or 0.0133
    6. 0.6300 or 0.6264

    1. X = the number of dealers she calls until she finds one with a used red Miata
    2. 0,1,2,3,...
    3. X~G(0.28)
    4. 3.57
    5. 0.7313
    6. 0.2497

    1. X = the number of shell pieces in one cake
    2. 0,1,2,3,...
    3. X~P(1.5)
    4. 1.5
    5. 0.2231
    6. 0.0001
    7. Yes

  8. Start by writing the probability distribution. X is net gain or loss = prize (if any) less $10 cost of ticket

    X = $ net gain or loss
    		P(X)
    $500 - $10 = $490
    		 1/100
    $100 - $10 = $90 2/100
    $25 - $10 = $15 4/100
    $0 - $10 = $-10 93/100
    Table 4.8

    Expected Value = (490)(1/100) + (90)(2/100) + (15)(4/100) + (-10) (93/100) of $2 per ticket, on average.


    • X = number of questions answered correctly
    • X~B(10,0.5)
    • We are interested in AT LEAST 70% of 10 questions correct. 70% of 10 is 7. We want to find the probability that X is greater than or equal to 7. The event "at least 7" is the complement of "less than or equal to 6".
    • Using your calculator's distribution menu: 1 -binomcdf(10, .5, 6) gives 0.171875
    • The probability of getting at least 70% of the 10 questions correct when randomly guessing is approximately 0.172


    • X = number of questions answered correctly
    • X-B(32, 1/3)
    • We are interested in MORE THAN 75% of 32 questions correct. 75% of 32 is 24. We want to find P(X>24). The event "more than 24" is the complement of "less than or equal to 24".
    • Using your calculator's distribution menu: 1 - binomcdf(32, 1/3, 24)
    • P(X>24) = 0.00000026761
    • The probability of getting more than 75% of the 32 questions correct when randomly guessing is very small and practically zero.