6.49 Let Y₁ be a binomial random variable with n, trials and probability of success given by p. Let Y₂ be another binomial random variable with n₂ trials and probability of success also given by p. If Y₁ and Y₂ are independent, find the probability function of Y₁ + Y₂.
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- The probability that data are entered incorrectly into a field in a database is 0.008. A data entry form has 24 fields, and errors occur independently for each field. The random variable X is the number of fields on the form with an error. Does X have a discrete uniform distribution? Why or why not?Q2 GX is the random variable such that X ~ B(15, p) and Var(X) = 2.4. Find the two possible values of p. 5) X is the random variable such that X ~ B(n, p), E(X) = 4.8 and Var(X) = 2.88. Find the values of n and p. | The probability that a salesman gets a reply when he knocks on the door of a house is 0.65. Find the probability that in a street of 10 houses he receives: i exactly 5 replies ii at least 5 replies. i How many houses should he visit such that the random variable X = 'number of replies' has a mean of 78? ii What is the variance in this case?Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?
- Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P ( X = 5 )4. A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Yı = 0, if the policy holder does not have any health issues; Yı = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).Suppose that the time. in days, required to repair a heat pump is a random variable X having a gamma distribution with parameters k = 8 and A = 2. What is the probability that on the next service call (a) at most 3 day will be required to repair the heat pump? (b) at least 2 days will be required to repair the heat pump? %3D %3D
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- Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T. What is the probability that Soledad sends more texts on a randomly selected day? 0.104 0.214 0.786 0.8961. Provide the graphs for PDF and CDF of the random variable B which takes on values of 1 and 0 with probability of 0.40 and 0.60. (Don't forget the horizontal axis must be sorted).Total blood volume (in mi) per body wight (in ke) is important in medical research. For healthy aduks, the red blood cell volume mean is about p = 28 ml/kg.t Red blood cell vokume that is too lom ar too high can indicate a medical problem. Suppose that koger has had seven blood tests, and the red blood cell volumes weré as follows Let x be a random variable that represents Roger's red blood cll volume. Assume that x has a narmal distributian and - 4.75. Do the data indicate that koger's red blood cell valume is different (either way) from a- 28 mi/kg? Use a 0.01 lervel of significance. a What is the leval of sigaicance State the null and alternate hypotheses. Will you use a left-lailed, right-laded, or two-tailed test? O H: - 28 ml/kg; H: 2s m/kg; Ima-tailed o Ho: - 28 ml/ka; H 28 m/ka, let-tailed O Ho: 28 mil/kg: H1:- 28 ml/kg; tmo-tailed O Ho: 28 m/ka, H > 28 m/kg; right-laiked (b) What sampling distribution wil you use? Explain the rationale for your choice of sampling distributian.…