where X1 , X2 , X3 are the three test scores and X is the final score. Assume that your test scores are (integer) values between 1 and 10 with equal probability 1/10, independently from each other. What is the probability mass function of the final score?
Q6. (10) The metro train arrives at the station, always on time, near your home every quarter hour starting at 6:00 AM. You walk into the station every morning between 7:10 and 7:30 AM, with the time in this interval being a uniform random variable.
The mean is the most commonly-used measure of central tendency in a distribution. The mean is valid only for interval data. Since it uses the values of all of the data points in the populations or sample, the mean is influenced by outliers that may be at the extremes of the data set. On the other hand, the median can be determined for ordinal data as well as interval data. Unlike the mean, the median is not influenced by outliers at the extremes of the data set.
Q8. (10) A system consists of 3 components arranged in series. The lifetime (in days) of each component follows approximately an exponential distribution with a mean lifetime of 100 days. The lifetimes of the components are independent.
Where p1(x, ), p2(x, ), p3(x, ) are three independent exponential distributions in parallel. After some algebra and if we take q as any of the three independent exponential distributions, q = p1 or q = p2, q = q3, q =