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18 December, 05:57

An investor holds two stocks, each of which can rise (R), remain unchanged (U), or decline (D) on any particular day. Assume that for the first stock (on a particular day)

P (R) = 0.2, P (U) = 0.6, P (D) = 0.2

and that for the second stock (on a particular day)

P (R) = 0.3, P (U) = 0.4, P (D) = 0.3

Assuming that these stocks move independently, find the probability that both stocks decline; the probability that exactly one stock rises; the probability that exactly one stock is unchanged; the probability that both stocks rise. (Round your answers to 2 decimal places.)

Both decline =

Exactly one rises =

Exactly one unchanged =

Both rise =

+3
Answers (1)
  1. 18 December, 06:22
    0
    1. 0.06

    2. 0.38

    3. 0.52

    4. 0.06

    Explanation:

    1) Both decline = P1 (D) * P2 (D)

    = 0.2 * 0.3

    = 0.06

    (stock 1 declines and stock 2 declines)

    2) Exactly one rises:

    = P1 (R) * [P2 (U) + P2 (D) ] + P2 (R) * [P1 (U) + P1 (D) ]

    = 0.2 * [0.4 + 0.3] + 0.3 * [0.6 + 0.2]

    = 0.14 + 0.24

    = 0.38

    (stock 1 rises and {stock 2 declines or remains unchanged})

    or (stock 2 rises and {stock 1 declines or remains unchanged})

    3) Exactly one unchanged:

    = P1 (U) * [P2 (R) + P2 (D) ] + P2 (U) * [P1 (R) + P1 (D) ]

    = 0.6 * [0.3 + 0.3] + 0.4 * [0.2 + 0.2]

    = 0.36 + 0.16

    = 0.52

    4) Both rise = P1 (R) * P2 (R)

    = 0.2 * 0.3

    = 0.06
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