Two random variables X and Y have joint char- acteristic function rl@,a)=exp(-20,? – 8m3) Show that X and Y are zero mean ran- (1) dom variables.
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- The spinner is spun one fime and a fair coin is tossed. Find the probabilities. P(R) = P(T) = %3D Yellow Red P(B U T)= P(G^) = Blue Green Sample Space: P(G N H)= P(Y U H)C = P(BC)= P(G NT)=A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball labeled with the number "3". Two balls are selected, without replacement. Let X be the total of the values on the two balls. Find the variance of X.It's desired to model the random variable X with a shape that rises to a peak near x=6 and whose possible values are integers 1-6. Copy paste the following lines of code into R: x <- 1:10 shape <- x*(12-x) barplot(shape, names. arg=x) This "shape" isn't a valid PMF because the numbers don't sum to 1. Convert the numbers in "shape" to valid probabilities and report P(X-5). Copy/paste all digits from R into your answer here.
- For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishOne of the major products at a large company is french fries that are sold on the commercial market to certain customers such as fast-food chains. French fries have numerous quality attributes that are important to customers. One of these is called "dark ends," which are the dark-colored ends that can occur when the fries are cooked. Suppose a major customer will accept no more than 0.06 of the fries having dark ends. Recently, the customer called the company saying that a recent random sample of 400 fries was tested from a shipment and 36 fries had dark ends. Assuming that the population does meet the 0.06 standard, what is the probability of getting a sample of 400 with 36 or more dark ends? Comment on this result. The probability of getting a sample of 400 with 36 or more dark ends is (Round to four decimal places as needed.)According to the Max Markwell classifica- tion, there are three types of drivers on High- way 71 between Bastrop, Texas and Austin, Texas: Good, Bad, and Egregious. 12% of all drivers are Good ●68% of all drivers are Bad • All remaining drivers are Egregious Good drivers drive in the passing lane 28% of the time (e.g., only while actively passing or making a left turn within the next 1/2 mile) • Bad drivers drive in the passing lane 74% of the time Egregious drivers camp in the passing lane 100% of the time. You observe a driver in the passing lane. De- termine the probability that the driver is a Bad or Egregious driver. NOTE: Round to the nearest whole percent. Answer in units of percent.
- The central limit theorem can be used to analyze round-off error. Suppose that the round-off error is represented as a uniform random variable on [-12,12]. If 100 numbers are added, approximate the probability that the round-off error exceeds (a) 1, (b) 2, and (c) 5.A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Calculator (These samples are chosen independently.) For the people taking Ripped, their sample mean is 9.76 with a sample variance of 11.67. For the people taking Gainz, their sample mean is 7.84 with a sample variance of 1.38. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.10 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? Perform a two-tailed test. Then complete…please be clear
- The table below shows head length and breadth of siblings. The four variables are X₁ = head length of first son, X₂ = head breadth of first son, X3 = head length of second son, and X₁ = head breadth of second son obtained from 25 families. Do first and second sons differ in their average head dimensions? State appropriate null hypothesis for this and test at a = 0.05 and interpret results. You may use softwares for computations but make sure to give (X₁-X3) all necessary details. Hint: Define Y = and state Ho in terms of Y. (X₂-X₁) Table 1: Head dimension data from Frets (1921), measured on siblings in 25 families X₁ X₂ 191 155 195 149 181 183 176 208 189 197 188 192 186 179 195 202 194 163 195 186 181 175 192 174 176 197 190 148 153 144 157 150 159 152 150 161 147 153 160 154 137 155 153 145 140 154 143 139 167 153 X3 179 201 185 188 171 192 190 189 197 187 179 183 174 190 188 161 183 173 182 165 185 178 176 200 187 X4 145 152 149 149 142 152 149 152 159 151 158 147 150 159 151 130…IF the mean of five observations is 8 and devietions of these observations about their mean ave -2,3,-5,0,4 Then the va lue of secound abservation is:Which value for X will result in the greatest relative frequency give discrete random variable X,when X~B(4,1/10)?