Statistics 4 BMQ Solutions (RVHS)

Statistics 4 Tutorial: Special DRV – Binomial Distribution Basic Mastery Questions With reference to the Learning Target Checklist, this question demonstrates Check point No. 1. On any given day, about 45% of the stocks on the Singapore Stock Exchange increase in value. Suppose four stocks are chosen. Let the discrete random variable X denote the number of stocks t hat increase in value. (a) Does X follow a binomial distribution? State any assumptions that you need to make. 6 (b) Suppose X follows a binomial distribution. Find the probability that: (i) exactly three of the stocks increase in value? 5a (ii) at least three of the four stocks increase in value? 5b 2. The random variable X has a binomial distribution with mean 8 and variance 8 3 . Calculate ( )P 10X  , giving 3 decimal places in your answer. 5b Solutions 1(a) X = Number of stocks (out of 4) that increase in value It might not be appropriate to assume X follows binomial distribution here because the increase in value among stocks is usually not independent, i.e. when one stock increases in value, the other stocks might be affected at the same time. If we want X to follow binomial distribution, we need to assume that - The event that a stock increases in value is independent of the event that another stock increasing in value. - The probability that a randomly chosen stock increases in value is constant, at 0.45 1(b) Suppose X follows a binomial distribution, then its distribution will be: ~ B(4,0.45)X (i) P(X = 3) = 0.200 (to 3sf) (ii) P(X ≥ 3) = 1 – P(X ≤ 2) = 1 – 0.759 = 0.241 (to 3sf)

2. The random variable X has a binomial distribution with mean 8 and variance 8 3 . Calculate ( )P 10X  , giving 3 decimal places in your answer. Solution: ~ B( , )X n p then 8.................(1) 8(1 ) .......(2)3 np np p = −= Solving, 2 , 123pn== . ( )P 10 1 P( 9) 0.181XX = −  =