8 children, called Felix, Lana, Adam, Shaa, Fred, John, Eric and Aral are playing a game where they make new words out of their first name initials.

a. What number of specific six-letter words that have two 'A' and two 'F' yet only one 'L' would they have the option to make out of their initials?

b. What number of specific six-letter words that have two 'A' and two 'F' (and no limits on 'L') would they have the option to make out of their initials?

NOTE: (The hidden of each individual should be used everything thought about once, that is, 'F', 'L' and 'A' and no more twice and 'J' and 'E' at most once; a word is here portrayed as a game plan of letters, regardless of whether it looks good in the English language.)

A researcher is investigating the effects of web learning on K-12 tutoring. He plans to

lead an examination that will be informed to all watchmen and teachers of understudies by the school

chiefs. He decides to subjectively pick four schools nearby with around

400 understudies. The watchmen and instructors of the overall large number of understudies at these schools will be outlined.

Portray the analyzing procedure being used and likely wellsprings of investigating inclination in his arrangement.

+7+

The game "craps" is played as follows: A player moves two sensible six-sided dice. If their total is 7 or 11 the player wins right away. If their all out is 2,3, or 12, the player loses right away. If their entire is some other number, this number transforms into the "point". The player by then more than once moves two dice until their entire reciprocals the point, wherein case the player wins, or counterparts 7, in which case the player loses. What is the probability of the player winning?

From past experience, Anna understands that the probability that her friend will take her to dinner in Oro Resto 0.7, the probability that they will watch movies is a 0.5, and the probability that he will take her to dinner or they will watch films is on 0.9 What is the probability that

a) They will do both

b) They will don't either?

4.A poker hand includes five cards. Overlooking the progression that these cards were overseen from a particularly modified deck of 52 playing a game, what is the probability of

a) three rulers or two sovereigns?

b) four red cards and one dim card? ..

..

Would the following statement be considered a valid one under the Bayesian or Frequentist views of probability and inference? "The probability that the average age of the class is greater than 25 is 15%" a. Valid from both a Bayesian and Frequentist perspective b. Invalid from both a Bayesian and Frequentist perspective c. Invalid from a Bayesian perspective, valid from a Frequentist perspective d. Valid from a Bayesian perspective, invalid from a Frequentist perspective8. 3] Bayesian Estimation vs MLE I) In Bayesian estimation, you start with a prior distribution p(0). Write down the equation that shows how you compute the posterior distribution p(0|D) where D is r1, 12, ....IN the collection of data that you see. II) In Bayesian estimation, how do you compute p(x|D) (your estimation of the pdf after seeing the data - i.e., a "prediction")? You may assume a parameter vector 0 that is a continuous random variable/vector that parametriza the probability density p(x|0) in your answer. P(: D) = III) In maximum likelihood estimation, how do you compute p(r D)? P(:|D) =1. A large retailer sells high fashion pants and must commit to specific production quantities for all of its pants several months in advance. Overestimating customer demand will result in unsold inventoryr vvhile underestimating customer demand will lead to stockouts. The retailer has used historical data, and current economic conditions to construct the following probabilistic forecast of the demand for a particular style of pants {note that the forecasted demand is normally distributed]: DemandIYEar {units} Probability 5,000 20% 6,000 10% 1000 40% 3,0 00 20% 9,000 10% The xed production cost is $50,000, the variable production cost per unit is $140, the selling price during the winter season is $400, and the salvage value for the pants not sold during the pant season is $30. a. Calculate the expected [or average] demand, based on the above probabilistic forecast Please show all your work. [4 points} b. Do you expect the optimal order gua ntity to be higher or lower than the expected [or average} demand? Why? Note: you do NOT need to determine the optimal order quantity in this section {you need to do that in part c}. [4 points] c. Determine the optimal order quantity. assuming that the standard deviation of the forecasted demand is 1,0 00. Please show all your work. {10 points]