cross-ied

The number of days a particular stock increases in a given five-day period is uniformly distributed between zero and five inclusive. In a given five-day trading week, what is the probability that the stock will increase exactly three days?

A) 0.333.

B) 0.167.

C) 0.600.

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If the possible outcomes are X0,1,2,3,4,5), then the probability of each of the six outcomes is 1 / 6 = 0.167.

cross-ied

The Night Raiders, an expansion team in the National Indoor Football League, is having a challenging first season with a current win loss record of 0 and 4. However, the team recently signed four new defensive players and one of the team sponsors (who also happens to hold a CFA charter) calculates the probability of the team winning a game at 0.40. Assuming that whether the team wins a game is independent of whether it wins any other game, the probability that the team will win 6 out of the next 10 games is closest to:

A) 0.417.

B) 0.112.

C) 0.350.

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Use the formula for a binomial random variable to calculate the answer to this question. We will define "success" as the team winning a game. The formula is:

p(x) = P(X = x) = [number of ways to choose x from n] × px × (1 - p)n-x,

where [number of ways to choose x from n] = n! / [(n - x)! × x!].
Here, p(x) = P(X = 6) = [10! / (10 − 6)! × 6!] × 0.406 × (1 − 0.40)10-6
= 210.0 × 0.00410 × 0.12960 = 0.11159, or approximately 0.112.
To calculate factorial using your financial calculator: On the TI, factorial is [2nd] ¡→ [x!]. On the HP, factorial is [g] → [n!]. To compute 10! on the TI, enter [10] → [2nd] → [x!] = 3,628,800. On the HP, use [10] → [ENTER] → [g] → [n!].