1 10 pts We bought a pack of 10 lightbulbs from a garage sale and collect a random sample of 2 lightbulbs no replacement and count the number of lightbulbs that are defective create a probability distribution for this discrete random variable a First define your random variable X the number of defective lightbulbs in a random The random variable X will be defined sample of 2 lightbulbs chosen without replacement from the pack of 10 bulbs X can take from values 0 to 2 where X 0 means both bulbs are working X 1 means one bulbs is working and X 2 means both bulbs are defective b Next showing work for all of your probabilities in the space below fill in the table below round probabilities to 4 decimal places X P X total of bulbs 10 of defective bulbs 6 of working bulbs 4 402 probability of 2 bulbs working 10 probability of 1 bulbs working probability c What do the probabilities sum up to P x 2 7 5 0 1333 6c 4c 10 6c2 of 2 bulbs working 10c 10C2 0 5333 0 6666 1 1999 33 15 1 0 5333 2 0 3333 0 3333 I Sum 1 P x 1 1 1 28 27 28 1 1 3 1 1 28 P x 0 2 ts d What is the expected number of defective lightbulbs in our sample P x 2 0 3333 0 3333 2 0 53331 0 1333 0 P x 1 0 5333 P x 0 0 1333 0 1333 0 5333 1 11 2 defective lightbulbs e Using technology find the standard deviation for the number of defective lightbulbs in our sample