1. If three coins are tossed, which is NOT a possible value of the randomvariable for the number of tails?A. 1B. 2C. 3D. 4 Show 2. Which of the following is a discrete random variable? Get answer to your question and much more 3. Which formula gives the probability distribution shown by the table?X34P(X)1/31/451/5 Get answer to your question and much more 4. How many ways can a "double" come out when you roll two dice? Get answer to your question and much more 5. It is a numerical quantity that is assigned to the outcome of an experiment.A. random variableB. variableC. probabilityD. probability distribution B. Classify the following random variables as discrete or continuous.1. The weight of the professional boxers2. The number of defective COVID-19 Rapid Antibody Test Kit3. The area of lots in an exclusive subdivision4. The number of recovered patients of COVID-19 per province5. The number of students with Academic Excellence in a school perdistrictC. Determine the values of the random variables in each of the followingdistributions.1. Two coins are tossed. Let H be the number of tails that occur.Determine the values of the random variable H.2. A meeting of envoys was attended by 4 Koreans and 2 Filipinos. Ifthree envoys were selected at random one after the other, determinethe values of the random variable K representing the number ofKoreans. A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.Discrete Random VariablesA discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function. (Definitions taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) Suppose a random variable X may take k different values, with the probability that X = xi defined to be P(X = xi) = pi. The probabilities pi must satisfy the following: 1: 0 < pi < 1 for each i 2: p1 + p2 + ... + pk = 1.Example The probabilities associated with each outcome are described by the following table: Outcome 1 2 3 4 Probability 0.1 0.3 0.4 0.2The probability that X is equal to 2 or 3 is the sum of the two probabilities: P(X = 2 or X = 3) = P(X = 2) + P(X = 3) = 0.3 + 0.4 = 0.7. Similarly, the probability that X is greater than 1 is equal to 1 - P(X = 1) = 1 - 0.1 = 0.9, by the complement rule. This distribution may also be described by the probability histogram shown to the right: All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable X is less than or equal to x, for every value x. For a discrete random variable, the cumulative distribution function is found by summing up the probabilities. (Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) ExampleThe probability that X is less than or equal to 1 is 0.1, the probability that X is less than or equal to 2 is 0.1+0.3 = 0.4, the probability that X is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and the probability that X is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1. The probability histogram for the
cumulative distribution of this random variable is shown to the right: Continuous Random VariablesA continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.(Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values, and is represented by the area under a curve (in advanced mathematics, this is known as an integral). The probability of observing any single value is equal to 0, since the number of values which may be assumed by the random variable is infinite. Suppose a random variable X may take all values over an interval of real numbers. Then the probability that X is in the set of outcomes A, P(A), is defined to be the area above A and under a curve. The curve, which represents a function p(x), must satisfy the following: 1: The curve has no negative values (p(x) > 0 for all x) 2: The total area under the curve is equal to 1.A curve meeting these requirements is known as a density curve. The Uniform DistributionA random number generator acting over an interval of numbers (a,b) has a continuous distribution. Since any interval of numbers of equal width has an equal probability of being observed, the curve describing the distribution is a rectangle, with constant height across the interval and 0 height elsewhere. Since the area under the curve must be equal to 1, the length of the interval determines the height of the curve.The following graphs plot the density curves for random number generators over the intervals (4,5) (top left), (2,6) (top right), (5,5.5) (lower left), and (3,5) (lower right). The distributions corresponding to these curves are known as uniform distributions. P(X < 3 and X > 5) = P(X < 3) + P(X > 5) = (3-2)*0.25 + (6-5)*0.25 = 0.25 + 0.25 = 0.5. The uniform distribution is often used to simulate data. Suppose you would like to simulate data for 10 rolls of a regular 6-sided die. Using the MINITAB "RAND" command with the "UNIF" subcommand generates 10 numbers in the interval (0,6): MTB > RAND 10 c2; SUBC> unif 0 6.Assign the discrete random variable X to the values 1, 2, 3, 4, 5, or 6 as follows: if 0<X<1, X=1 if 1<X<2, X=2 if 2<X<3, X=3 if 3<X<4, X=4 if 4<X<5, X=5 if X>5, X=6. Use the generated MINITAB data to assign X to a value for each roll of the die: Uniform Data X Value 4.53786 5 5.77474 6 3.69518 4 1.03929 2 4.23835 5 0.37096 1 0.75272 1 5.56563 6 0.89045 1 3.18086 4 Another type of continuous density curve is the normal distribution. The area under the curve is not easy to calculate for a normal random variable X with mean Which is not a possible value of a random variable?Random variables can only have one value. The probability of the value of a random variable could be zero. The sum of all the probabilities in a probability distribution is always equal to one.
What are the possible values of the random variable for the number?Example: Let X be the outcome of the roll of a die. Then X is a random variable. Its possible values are 1, 2, 3, 4, 5, and 6; each of these possible values has probability 1/6.
Which of the following is not true for a random variable?This is Expert Verified Answer
Random variable can only have one value" is not true. A variable in an equation can satisfy the equation such that its value is zero. So, it is possible that the value of a random variable is zero. A random can have a single value but it is not necessary that it only has one value.
What are the 3 types of random variable?There are three types of random variables- discrete random variables, continuous random variables, and mixed random variables.
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Which of the following is not a possible value of the random variable for the number?
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