- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution

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**CFA Practice Question**

The probability that the price of a stock increases is 0.30. The price of the stock will either increase or decrease each day independently of what happened on the previous day. An experiment consists of observing the price of this stock during a 30-day period. What are the expected value and the variance of the number of days that the stock price increases?

A. 6.3; 9

B. 9; 6.3

C. 9; 15

**Explanation:**Assume X denotes the random variable for the number of days that the stock price increases. X ~ Bin(30, 0.3) therefore, E(X) = 30 x 0.3 = 9 and V(X) = 30 x 0.3 x (1 - 0.3) = 6.3.

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**User Contributed Comments**
4

User |
Comment |
---|---|

tanyak |
Why is variance calculated this way? |

labsbamb |
When u have a binomial function F(x) E(x)= X*P V(x)=X*P*(1-P) |

Mariecfa |
Binomial Mean or Expected Value = n*p n=30, p=0.30, E(X)= 30*.30=9 Binomial Variance = n*p*(1-p) Variance=30*.30*.70=6.3 Binomial Standard Deviation = Square root of [n*P*(1-p)] |

dream007 |
30 days? thought we only trade 5 days a week! |