| November 24, 2016
  • The incomes of all families in a particular suburb can be represented by a continuous random variable. It is known that the median income for all families in this suburb is $60,000 and that 40% of all families in the suburb have incomes above $72,000.

    a) For a randomly chosen family, what is the probability that its income will be between $60,000 and $72,000?

    b) Given no further information is available, what can be said about the probability that a randomly chosen family has an income below $65,000?

    A portfolio manager has asked you to analyze a newly acquired portfolio to determine its value and variability. The portfolio consists of 50 shares of Alpha Music and 40 shares of Beta Shows. Analysis of past history indicates that the share price of Alpha Music has a mean of $25 and variance of 121. Similarly, Beta Shows has a mean share price of $40 with a variance of 225. Your best evidence indicates that the share prices have a correlation coefficient of +0.5.

    a) Compute the mean value and variance of the portfolio.

    b) If the correlation coefficient between the share prices were actually – 0.5, what would be the mean value and the variance of the portfolio?

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