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June 2017 p62 q7
3065
During the school holidays, each day Khalid either rides on his bicycle with probability 0.6, or on his skateboard with probability 0.4. Khalid does not ride on both on the same day.
There are 45 days of school holidays. Show that the variance of the number of days Khalid rides on his skateboard is the same as the variance of the number of days that Khalid rides on his bicycle.
Solution
Let the number of days Khalid rides his bicycle be a binomial random variable with parameters 45 and 0.6. The variance is given by:
\(\text{Var}(B) = 45 \times 0.6 \times 0.4\)
Similarly, let the number of days Khalid rides his skateboard be a binomial random variable with parameters 45 and 0.4. The variance is given by:
\(\text{Var}(S) = 45 \times 0.4 \times 0.6\)
Since \(\text{Var}(B) = \text{Var}(S)\), the variances are the same.