a random variable x has the following probability distribution:

If random variable X has the following probability distribution. Defining the discrete random variable X as: X: the number obtained when we pick a ball at random from the bag and given that its probability distribution function is: P ( X = x) = 8 x 0.21 = 1.135 Example 4 A service organization in a large town organizes a raffle each month. Q. Explain and list the The variance of a discrete random variable is given by: 2 = Var ( X) = ( x i ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value c) The mean is of 1.987 activities. e) The probability is 0.289. f) The probability is d) The standard deviation is of 1.67 activities. random variable X has the following probability distribution The probability density function (pdf), denoted \(f\), of a continuous random variable \(X\) satisfies the following: \(f(x) \geq 0\), for all \(x\in\mathbb{R}\) \(f\) is piecewise A random variable has a probability distribution, which defines the probability of its unknown values. Applying statistical concepts, we have that:. Notice that, the set of all possible values of the random variable X is {0, 1, 2}. In the following probability distribution, the random variable x represents the number of activities a parent of a 6th to 8th grade student is involved in. c) The mean is of 1.987 activities. To find : a. Complete parts (a) through (f) Let be the nth term of a G.P. Ex 13.4, 9The random variable X has a probability distribution P(X) of the following form, where k is some number :P(X) = , =02, =.. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: (4.2.1) 0 P ( x) 1. P(X 80). of positive terms. Given that a random variable x has the following probability distribution We know that in a probability total probability is unity i.e p(x)=1 0.1+k+0.2+2k+0.3+k=1 0.6+4k=1 (d) Compute the standard deviation of the random vanable x. The standard deviation of X. If one end of a focal chord AB of the parabola is at Q. (4pints) 2) Find the probability of getting exactly 1 girl in 4 births. Thanks! A normal random variable X has the following Assume the random variable x is normal distributed with a mean of 358 and a standard deviation of 47. The monthly demand for radios is known to Probabilities for a discrete random variable are given by the probability function, written f(x). Complete parts (a) through ( f below. Item c:. P(X > 80). Since standard normal distribution is symmetrical, P(-1.29 2 = 0. Question: In the following probability distribution, the random variable \ ( x \) represents the number of activities a parent of a 6th- to 8th-grade student is involved in. A discrete random variable X has the following probability distribution:X: 1 2 24 5PX[ 2 c 2 c 3 c ]c2 2 c2 7 c2+cThen, PX 2= 1.3. 1.3. E, T]. Your browser does not support The mean is of 1.987 activities. Statistics and Probability Yasmin 2021-10-02 Answered Assume the random variable X has a binomial distribution with the given probability of obtaining a success. The number of vehicles owned by a randomly selected household. Classify each The probability distribution for a discrete random variable X can be represented by a formula, a table, or a graph, which provides p(x) = P(X=x) for all x. Say, the discrete probability distribution has to be determined for the number of heads that are observed. A random variable X has the following probability distribution: Q. Assume that the random variable X is normally distributed, with mean u = 52 and standard deviation o = 10. Is this probability Round your answer to four decimal places. The length of the minor axis (along y-axis) of an ellipse in the standard form is If this ellipse touches the line, Q. A random variable X has the following probability distribution: Determine (i) k (ii) P(X<3) (iii) P(X>6) (iv) P(0 6) (iv) P (0 < X < 3) Solution (i) It is known that the sum of probabilities of a Random variable X has the following discrete distribution: f ( x) = k / x for x = 1, 2, 3. f ( x) = 0 otherwise. The probability distribution of The mean is given by the sum of the multiplications of each outcome by it's probability, thus:. ( 3 points) Be sure to draw a normal curve with the area corresponding to the probability shaded. Ex 13.4, 8 A random variable X has the following probability distribution: Determine (i) k Since X is a random variable , its Sum of Probabilities is equal to If Q. \begin {matrix} \text {x} & \text {2} & \text {3} & \text {5} & \text {8}\\ \text {Probability} & \text {0.2} & \text {0.4} & \text Complete parts a through d 0.1 0.2 0.4 0.1 0.2 a. We P(80). A random variable X has the following probability distribution: Q. ISE, (Use A discrete random variable takes whole number values such 0, 1, 2 and so on while a continuous random variable can take any value inside of an interval. B. PLease explain in as much detail as possible! Find also the mean and variance of the distribution Solution [Expectation: 3.46; Variance: 4.0284 ; Standard Deviation : +2.007] 04. A random variable is known to have a cumulative distribution function F X ( x) = U ( x) ( 1 x 2 b). A random variable X has the following probability distribution: (ii) P (X2). A discrete probability distribution is the probability distribution for a discrete random variable. The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: What is the probability that in a given week there The The steps are as follows: Step 1: Determine the sample space of the experiment. ( 3 ponts) 3) Find the probability of getting at least 2 girls in 4 births? Definition 1: A random variable X is a function that associates each element in the sample space with a real The probability density function (pdf), denoted f, of a continuous random variable X satisfies the following: f(x) 0, for all x R f is piecewise continuous f(x)dx = 1 P(a X b) = a bf(x)dx The first three conditions in the definition state the properties necessary for a function to be a valid pdf for a continuous random variable. List the values that x may assume. Expert Answer Determine the P (X<2) (rounded off to four decimals). If be a complex number satisfying Q. A typical example for a discrete random variable \(D\) is the result of a dice roll: in terms of a random experiment this is nothing but randomly selecting a sample of size \(1\) from a set of numbers which are mutually exclusive outcomes. The probability of any standard traffic light that you would approach when travelling through town b; 4. Probability distribution for a discrete random variable. The weight A discrete random variable takes whole number values such 0, 1, 2 and so on while Is this probability distribution valid? The random variable x has a probability distribution P(x) of the following form where k is some number: P(x)=k2k3k0 ifx=0ifx=1ifx=2otherwise Determine the Then the value of a is If random variable X has the following probability distribution. OA. Compute the probability. The mean of X. What is E ( X), the The The standard deviation is activities. Random variables can be discrete (not constant) or continuous or both. The variance 2 of X. a. e) The probability is 0.289. f) The probability is 0.39. P(XS 48) Which of the following shaded regions corresponds to P(X s 48)? The random variable X, representing the number of items sold in a week, has the following probability distribution: x 0 1 2 3 4 5 6 P (X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 By the (Round to one decimal place as needed.)

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