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Math Help - Probability

  1. #1
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    Probability

    4) There are 1000 tickets for a lottery. The lottery take s place every week, and every week prizes are given away: one for the first price, which is worth $10,000 and 3 second prizes of $2000 each one. You have a ticket for this week's lottery. leEt the random variable X, which mesures the amount of prize money that you will receive after the lottery is given away according to the following info:

    P{X=0} = 0.996
    P{X=2,000} = 0.003
    P{X=10,000} = 0.001


    -What is the probability that you will receive at least $2000?
    - Find the expected value and the standard deviation of X
    -You decided to buy 20 tickets for the next 20 lotterias. Let Y be the random variable that measures the number of times that you get a prize. WHat is the expected # of times that


    2) The temperature of a solid is measured by two devices. With the first deice, the expected temperature is t with a standard deviation of 0.8. WIth the second one, the expected temperature is t with an std deviation of 0.3. Which device measures the temperature better? explain?
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    Quote Originally Posted by Andreamet View Post
    4) There are 1000 tickets for a lottery. The lottery take s place every week, and every week prizes are given away: one for the first price, which is worth $10,000 and 3 second prizes of $2000 each one. You have a ticket for this week's lottery. leEt the random variable X, which mesures the amount of prize money that you will receive after the lottery is given away according to the following info:

    P{X=0} = 0.996
    P{X=2,000} = 0.003
    P{X=10,000} = 0.001


    -What is the probability that you will receive at least $2000? Mr F says: 0.003 + 0.001 = 0.004.

    - Find the expected value and the standard deviation of X

    Mr F says: E(X) = (0)(0.996) + (2,000)(0.003) + (10,000)(0.001) = .....

    E(X^2) = (0^2)(0.996) + (2,000^2)(0.003) + (10,000^2)(0.001) = .....

    Standard deviation = square root of variance. Variance = E(X^2) - E(X) = ....


    -You decided to buy 20 tickets for the next 20 lotterias. Let Y be the random variable that measures the number of times that you get a prize. WHat is the expected # of times that Mr F says: (20) (0.004) = 0.08.
    [snip]
    ..
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  3. #3
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    Quote Originally Posted by Andreamet View Post
    4) [snip]
    2) The temperature of a solid is measured by two devices. With the first deice, the expected temperature is t with a standard deviation of 0.8. WIth the second one, the expected temperature is t with an std deviation of 0.3. Which device measures the temperature better? explain?
    Device 2. Smaller standard deviation ...... (look at the definition of standard deviation to understand why smaller is better)
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