Statistics Week 9 Graded Assignments IIT Madras

1.A discrete random variable $X$ can take the values 1,2,···,7. For these values the cumulative distribution function is defined by:$F(x)=P(X\le x)=\genfrac{}{}{0ex}{}{x^2+k}{95}$; $x$= 1,2,···,7. Find the value of $k$.

2.An organization in Texas organizes lucky draw this month. 3 thousand tickets are sold for 2$ each. Each has an equal chance of winning. 1 tickets will win 698$, 3 tickets will win 353$ and 4 tickets will win 63$. Let, the random variable $X$ denote the net gain from purchase of one ticket. What is the probability that $X$ takes the value less than 353? (Enter the answer correct to 4 decimal place)

3. In a group of 204 people, 29 are photographers and 175 are journalists. 12 people are randomly picked from a group of these 204 people. Let, $Y$ be a random variable which represents the number of photographers. How many possible values can the random variable $Y$ take?

6. Nina has 6 music sessions in a week. She attends the sessions 6 days a week 59% of the time, 5 days 13% of the time, one day 7% of the time, and no days 21% of the time. Let, $X$ be a discrete random variable representing the number of sessions she attends in a week. Suppose one week is randomly selected, what is the probability that the random variable $X$ take the value at most 5?(Enter the answer correct to 2 decimal places)

7.Find the value of k for which k${\left(\genfrac{}{}{0ex}{}{4}{7}\right)}^x$( x = 0, 1, 2, …) is a pmf.(Enter the answer correct up to 2 decimal places)

8.Using the information in previous question, calculate $P(X=2)$.(Enter the answer correct up to 2 decimal places)

9.From a box $A$ containing 3 white and 6 black balls, 5 balls are transferred into an empty box $B$. Let $X$ be a random variable that represents the number of white balls which are transferred from $A$ to $B$. What value of random variable will have the least probability?

10. The probability mass function of a random variable X is given by:

       $P(X=x)$= $\{\begin{array}{ll}3k^2-3k& \text{for }x=0\\ 2k^2-1& \text{for}x=1\\ 0& \text{otherwise}\end{array}$

 Determine the value of k given $k>0$.