A random variable X has density 3x2 for 0 < x < 1.  Find its variance. (use a decimal number, rounded to the nearest 1,000th. For example, 0.123)

Suppose you would like to keep a test tube at 48F (exactly), but your refrigeration unit exhibits some random fluctuations, so that the difference between the temperature at which you set the thermostat and the true temperature is distributed normally with mean 0 and variance 1.96. What is the highest you can set the thermostat and be 95% sure that the true temperature is no more than 48F?

The lifetime X of a certain electronic component in hours is an exponential random variable with a mean of 4.3. Determine the variance of X. The answer should be a number rounded to five decimal places,

4. Review the variance function for specific distributions. For Bernoulli, Poisson, Gamma, and Inverse Gaussian, what does the variance function say about our ability to predict the range of possible values? (This may be a little bit challenging; give it your best guess.)

The amount of nicotine in a cigarette produced by a tobacco company is a random variable with mean 2.2 mg and standard deviation 0.3 mg. Taking 100 randomly chosen cigarettes, let X; denote the nicotine content of the ith cigarette for i = 1,..., 100, and let X = 100 Ei=1 X; be the sample mean of the nicotine content. 100 a. What is the variance of X? Var(X) = Approximate the probability that X is higher than 2.25 in terms of the standard normal random variable. (The answer is given in terms of 2.25, standardized by mean and standard deviation of X.) P(X> 2.25) = P(Z >

please answer.

The weight of cereal boxes (y) follows a normal distributed with a variance of 0.1 squared ounces. If the average is 15.8 ounces, then P(y < 16) = If the average is 16.5 ounces, then P(y > 16.2)

Find the variance of x or the number of cups of coffee. (Do not round intermediate steps but round your final answer to 4 decimal places)

Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the z-value for a score of 80? -2.0 -0.4 1.0 2.0 0.4

Show the solution behind the answers for the questions.