6- The variance of the sum of the random variables equals the sum of the variances if the random variables are uncorrelated.
Q: Give two ways to compute the variance of a continuous random variable.
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Q: TRUE OR FALSE For a Binomial random variable, it can only takes on two possible values, 0 or 1.
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Q: How can we use discrete random variables in statistics?
A: Solution: Discrete random variable: A variable is said to be discrete if it takes the positive…
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Q: How can the sample covariance be used to estimate the covariance of random variables?
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Q: A continuous random variable can take on only specific, distinct values. True or False
A: A continuous random variable can take on only specific, distinct values.True or False
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Q: If the variance of the discrete random variable X = 36
A: Variance is 36
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Q: Why do we calculate sums of squares to find variance?
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Q: Define the Mean and Variance of Sums of Random Variables?
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Q: How to find the mean of the random variable x
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- What is the Weakness of Variance?3-Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You intially don't know the probability of success in a single experiment. But you know that, if you continue to run the experiment several times, the expected number of experiment required for the first success is 25. What is the variance of the number of experiments required for the first success?
- Show that (1) the mean value of a weighted sum of random variables equals the weighted sum of the mean values and (2) the variance of a weighted sum of N random variables equals the weighted sum of all their covariances.In a class of 50 students, every student took a certain a test which was out of 100 marks. Among all the students, 40% of them got 80, 30% of them got 72, 20% of them got 61 and rest of them got 53 marks. i. What is the expected mark of a student taking that test? ii. What is the expected mark of a student if he/she takes the test thrice? iii.What is the variance of marks of a student?The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is
- Suppose that we have disjoint normal populations A and B with equal population variances. Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance. If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?Which one is correct?A toy factory is planning to purchase two machines for their production. Machine A produces 5 toys on average with 1 unit of variance in 1 hour. Machine B, on the other hand, produces 10 toys on average with 3 units of variance in 2 hours. What is the expected number of toys at most could be produced among all combinations of machine A and B in 2 hours?
- 4 Thirty five percent of the students in a class of 100 are planning to go to graduate school, Find the variance of this binomial distributionI have 3 chickens where each of these chickens lays an egg with the probability 3/4 (independently). I sell each egg the chicken has laid for 8 coins. Work out the variance of the number of coins recieved.Rods are produced in large quantities in a factory. The masses of these rods are normally distributed with mean 250g and variance 9g. A random sample of 100 rods is selected. Find the probability that the mean mass of the rods in the sample will lie between 249g and 251g. If the rods are produced in batches of n and a batch is selected at random, find the least value of n such that the probability that the mean mass of the rods in the batch will lie between 249g and 251g is greater than 0.95.