Given the following PDF i 65.2 12.3 60.1 63.9 61.2 p_i 0.11 0.1 0.17 0.06 0.56 what is E[X]?
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- There was a compete e^AT partAn SRS of 100 flights by Speedy Airlines showed that 64 were on time. An SRS of 100 flights by Happy Airlines showed that 80 were on time. Let pS be the proportion of on-time flights for all Speedy Airline flights, and let pH be the proportion of all on-time flights for all Happy Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses H0 : pS – pH 0, Ha : pS – pH 0. The P-value of your test is 0.0117. Which of the following is an appropriate interpretation of the P-value? a. If the on-time rates for the two airlines are equal, there is a 0.0117 probability of getting samples with a difference as far or farther from zero as these samples. b. If the on-time rates for the two airlines are not equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.9883. c. The probability of making a Type I error is 0.0117. d. The probability of making a Type II error…For c in R, calculate E[e^cX] where X is exponential distribution.
- A tax accountant would like to test the claim that the proportion of individuals who owe when filing their taxes is greater than 0.20. If the z− test statistic was calculated as z=1.94, does the tax accountant have enough evidence to reject the null hypothesis? Assume α=0.05.An interval within which we expect 95% of all xx's to fall can be defined for any population by applying the ?3. If X has an exponential distribution with λ=2. Calculate the following P(X≤0)=? P(X≥2)=? P(1<X<2)=? The value of x such that P(X<x)=0.05 corresponds to x=?
- Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0Let X and Y are independent and both have exponential distribution,Find ??(?) , if Z=X+Y. Where PDF of X and Y are given as,??(?) = ??−???(?) and ??(?) = ??−???(?).A researcher conducts a hypothesis test using a sample of n = 20 with M = 34 and s 2 = 36 from an unknown population. What is the df value for the t statistic?
- Let {Xi} from i to n be IID from Bernoulli(p). Find the MQ estimator of p.A medical researcher says that less than 84% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 400 adults in that country, 81% think that healthy children should be required to be vaccinated. At α=0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below.Show that the following are probability density functions (pdf’s):