Suppose X has probability distribution, x: 0 1 2 3 4 P(X = x) 0.2 0.1 0.2 0.2 0.3 Find the following probabilities: a. P(X < 2) b. P(X ≤ 2 and X < 4) c. P(X ≤ 2 and X ≥ 1)

Pr. 3 Production. In a production process, let N mean "no trouble" and T"trouble." Let the transition probabilities from one day to the next be 0.8 for N ->>> N, hence 0.2 for N ->>> T, and 0.5 for T → N, hence 0.5 for T→ T. If today there is no trouble, what is the probability of N two days after today? Three days after today?

Could you please answer d and e.

Ahmed recently caught Covid-19. He had contact to 7 persons. Let X be the number of persons he infected, a discrete random variable. The probability distribution of X is as follows: 1 2 3 4 7 P(X) 0.079 0.203 0.079 0.118 0.28 0.021 0.01 0.21 Find the following probabilities (in 3 decimal places): (a) What is the probability that he infected more than 3 persons? (b) What is the probability that he infected 8 persons? (c) What is the probability that he did not infect anybody?

Determine the following probabilities.   a. For n=5 and π=0.12​, what is P(X=0​)? b. For n=9 and π=0.40​, what is ​P(X=8​)? c. For n=9 and π=0.60​, what is ​P(X=7​)?

Let the variable Z stand for a standard normally-distributed variable. Find these probabilities  a. p (z < 1.76 ) b. p ( -2.05 < z < .66 ) C. p ( z > -1.62 ) Then, find these z values that satisfy the following conditions a. 87.29% of the area under the distribution curve is to the left of it b. 67.72% of the area under the distribiution curve lies to the right of it

The following table lists the probability distribution of the number of patients entering the emergency room during a 1-hour period at a local hospital Use the table to find the following probabilities a)P( X=1) b)P(X ≥3) c)P(X <2)

Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. 23 4 y p(y) 0 1 0.61 0.21 0.11 0.05 ? (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) p(4) = (b) How would you interpret p(1) = 0.21? O In the long run, the proportion that will have at most one broken egg will equal 0.21. The proportion of eggs that will be broken in each carton from this population is 0.21. O In the long run, the proportion of cartons that have exactly one broken egg will equal 0.21. O The probability of one randomly chosen carton having broken eggs in it is 0.21. (c) Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs. P(y ≤ 2) = = Interpret this probability. O The proportion of eggs that will be broken in any two cartons from this population is this probability. O In the long run,…

Please do the second part

Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.0005 5 0.0033 6 0.0155 7 0.0532 8 0.1329 9 0.2362 10 0.2835 11 0.2062 12 0.0687 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x=7)=P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x≤7)=P(x≤7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? no yes