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Using the same data above.
A.Compute and interpret the mean of the random variable x.
B. Compute and interpret the standard deviation of the random variable x.
- Discrete random variable) Suppose a grocery store sells 6 containers of skim milk at the wholesale price of $1.15 per container and sells it for $1.65 per container. After the expiration date, the unsold milk is removed from the shelves and the seller receives a refund of three- fourths of the wholesale price for this item. The probability of the number of containers sold from this lot is shown in the table below: X f(x) 0 1/15 1 2/15 2 2/15 3 3/15 a. Calculate the probability of selling less than 3 containers. b. Calculate the expected number of packages sold. c. Calculate the expected utility and its standard deviation. 4 4/15 5 2/15 6 1/15Consider a discrete random variable, X. Identify the correct statement for using the cumulative distribution function (cdf), F(x), to solve the probability below. P(X> 5) 1-F(5) F(5) - F(4) F(6) - F(5) F(6) F(4) F(5) None of the above. 1-F(4)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 SC
- Find E(x) and Var(x) of X, where X is the discrete random variable whose probability table is given below. outcome Probability 1 3 4 7 0.2 0.5 0.1 0.2A 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).1/2 ,7/8 , 3/4 , 1
- 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…
- 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) =Is X a random variable if it has a probability distribution. Why or why not? x P(X=x) 1 0.45 2 0.31 3 0.29