(a) Construct a discrete probability distribution for the random variable x. (games played P(x)
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A.Compute and interpret the
B. Compute and interpret the standard deviation of the random variable x.
- Do you carpool? Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows. tab H ps lock esc Part: 0 / 7 → fn 14 Part 1 of 7 Skip Part r. design. (a) Find P (2). P (2) = . ! Ⓡ 1 2 3 4 5 P(x) 0.63 0.13 0.11 0.02 0.11 1 Type here to search ? Q x A Send data to Excel — Check Z @@ 2 X W S # 3 E IL X 5 alt D $ JOI 4 C O R % F 5 T V 40 Pa G 6 "4 B & Y 99+ hp 7 a H 4+ 8 N Save For Later © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | 144 9 tvo M 11 ULO 1 JK W LLL O 70- 441 L P : ; { alt ? Privacy Center DE = [1 Submit Assignment Accessibility 40 9:21 PM 2/21/2023 insert 1 1 . 4 1 prt sc C 屈 ola backspace pause ctri USE YOUR SMARTPHONE FOR Reviews Videos Featu Specs Support C 04 SCDirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by x 0 1 2 3 4 Px 0.34 0.39 0.17 0.06 0.04 1. Find P(3) 2. Find P(2 or fewer). 3. Find the probability that the standard is exceeded on at least one day. 4. Find the probability that the standard is exceeded on more than one day. 5. Compute the mean ux. Round the answer to two decimal places. 6.Compute the standard deviation σx. Round the answer to three decimal places.A random variable X has a following probability function, X 0 1 3 4 5 6 P(X) 0k 2k 2k | 3k k 2k 7k2 + k Find the value of, (i) k (ii) P(X < 6).
- A discrete random variable Y has the probability function as given below. Y -2 2 4 P(Y) 0.25 0.50 0.25 If F(Y) denotes the cumulative distribution function for Y, select the correct statement below Group of answer choices F(-3) = 0, F(1)=0.25 and F(3)=0.50 F(-3) = 0, F(1)=0.25 and F(5)=0 F(-3) = 0, F(0) = 0.25 and F(5) = 1 F(-3) = 0, F(1)=0.25 and F(6)=0 F(0)= 0, F(1)= 0 and F(3)=0The probability distribution of the random variable X is given in the following table. Random variable, x -2 -1 0 1 2 3 P(X = x) 0.10 0.15 0.05 0.20 0.15 0.35 Find the following probabilities. (a) P(X = 0)(b) P(X ≤ 0)(c) P(-1 < X ≤ 4)(d) P(X ≥ 1)Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X X 0 1 2 3 4 P(x) 0.35 0.38 0.91 0.05 0.03 Find p(1) Find (2 or fewer) c.Find the probability that the standard is exceeded on at least one day. Find the probability that the standard is exceeded on more than one day Compute the mean . Round the answer to two decimal places. (f) Compute the standard deviation . Round the answer to three decimal places. Relax! A recent survey asked people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 0.112 185 336 249 315 229 150 33 60 Total 1669 2. Consider these 1669 people to be a population. Let Xbe…
- K The probability of event A, given that event B has occurred, can be found using Bayes's Theorem. P(A) P(BA) P(A) P(B) A) + P(A) -P(BA) P(A| B)=- Use Bayes's Theorem to find P(A| B) using the probabilities shown below. P(A) = 0.25, P (A') = 0.75, P(B| A) = 0.1, and P(B| A') = = 0.5 The probability of event A, given that event B has occurred, is (Round to the nearest thousandth as needed.)Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by 0 P(x) 0.35 X Send data to Excel Part 1 of 4 (a) Find P (3). 1 2 3 0.38 0.19 0.05 0.03 P (3)= 0.05 Part: 1 / 4 Part 2 of 4 (b) Find P (3 or fewer). P (3 or fewer)= 4 = XLet 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. y 0 1 2 3 4 p(y) 0.63 0.19 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) = Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs. P(y ≤ 2) = Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. P(y < 2) =