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(a). The random variable X is the number of siblings of a student selected at random from Professor Appiah's Introductory Statistics class. It's probability distribution is given in the following table.
x
0
1
2
3
4
5
P(X=x)
1/4
1/3
1/6
7/48
1/16
1/24
Find the following
(i). The expected value of the random variable X.
(ii).The standard deviation of the random variable X.
(iii).The variance of the random variable X.
(b).Let Y represents the number of Boys in families having three children. List all possible birth order permutations for families having three children and give the value of Y for each outcome and their associated probabilities [Hint: a family of three is made up of Boys and Girls]. Use your probability distribution to find the following
(i). The mean of the random variable Y.
(ii).The standard deviation of the random variable Y.
(iii).The variance of the random variable Y.
Draw the pmf of the Poisson distribution that results when the parameter α is equal to the following:
A box contains 3 blue marbles and two red marbles. If two marbles are drawn randomly and without replacement, find the probability that (a) at least one of the marbles is blue
How many more sheep should be included in the sample if we want to say with 98% confidence that the population mean weight of the Jacob sheep is within 2.0 lb of the sample mean?
At a 5% level of significance, is there enough evidence from this survey to conclude that more than half of all adults would rather have $100 than a day off?
Compute a value V that enables us to state, with 90 percent confidence, that population variance (sigma^2) is less than V.
Suppose a random sample of 600 credit card users is taken. What is the probability that more than 150 credit card users are very close to the total limit on their card(s)?
question a statistics instructor is interested in the correlation pearson r between how many hours a student sleeps
Find the first order statistics at time instance 3. Find the probability at time instance k,the person is at the location m steps to the right of the origin.
question the events x and y are mutually exclusive. suppose px .05 and py .02. what is the probability of either x or
A student wants their College to offer Kickboxing classes as a Physical Education class. To justify that the class is desired he surveys 200 students and finds that 56% would be interested in taking the class.
Suppose you toss ten coins and count the number of heads. What is the probability that the number of heads you count will lie within two standard deviations of the mean?
A random sample of 11 health maintenance organizations (HMOs) was selected. For each HMO, the co-payment (in dollars) for a doctor's office visit was recorded. The results are as follows:
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