let X be a random variable and X-B(9,0.49) find the mean (expected value) of the random variable X

A random variable represents the number of successes in 10 Bernoulli trials, each with probability of success p= 0.65. (A) Find the mean and standard deviation of the random variable. (B) Find the probability that the number of successes lies within 1 standard deviation of the mean. (A) The mean of the random variable is (Type an integer or a decimal.)

Let X be the Random Variable: x 0 1 2 = x) P(X= 0.5 0.2 0.3 Let X1, X2 be the identically distributed Random Variables so that X1, X2 ~ X. Find the expected value and variance of both X and X1 + X2.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 62.0 kg and standard deviation ? = 9.0 kg. Suppose a doe that weighs less than 53 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2400 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 59 kg. If the average weight is less than 59 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 59 kg…

• The expected value of x is (enter an exact decimal in 0, 1). • The variance of x is (enter a decimal rounded to the third decimal place).

A student takes a test in which they have to indicate whether each of n statements is true or false. The student knows nothing at all about the subject matter and guesses the answers randomly. Let X denote the number of correct answers (a) Write down expressions for the expectation, E(X), and the variance, var(X). Suppose the student gets three marks for every correct answer but loses one mark for every incorrect answer. Let Y denote the student’s total score. (b) Show that Y = 4X −n. (c) Write down expressions for E(Y ) and var(Y ).

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean u = 57.0 kg and standard deviation o = 7.9 kg. Suppose a doe that weighs less than 48 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 55 does should be more than 54 kg. If the average weight is less than 54 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average welght x for a random sample of 55 does is less than…

I need help with d

You are to roll a fair die n=108  times, each time observing the number of dots appearing on the top side of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,108. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die.μXi= ____________ Enter your answer using all the decimals you can.σXi= ____________ Enter your answer using all the decimals you can.   (b) What is the probability that the average topside on your  tosses will be somewhere between 3.4 and 3.7? Enter your answer using all the decimals you can. _____________ (c) What is the probability that the average of your  tosses is greater than 4.15? Enter your answer using all the decimals you can. ______________

Let be a normally-distributed random variable with mean u= 100 and variance 2 = 16: Select which statement is true. P(94 < X< 106) = 0.68 approximately. P(92 < X< 108) = 0.68 approximately. P(86 < X<114) = 0.68 approximately. none of these P(96 < X< 104) = 0.68 approximately.