Math Answers

. Define the kernel and the image of a linear transformation M : V → W and hence Show that the Kernel and image of M are vector subspaces of V and W respectively. 

Define a vector subspace of a vector space V

Show that if P and Q are vector Subspaces of a vector space V then P ∩ Q is also a vector subspace of V.

Define a vector subspace of a vector space V

Define the kernel and the image of a linear transformation K : M → N and hence Show that the Kernel and image of K are vector subspaces of M and N respectively

233.8 316.5 284.6247.3 317.6 280.3 231.9 255.3 258.4 276.9 278.9 269.3 263.9 289.3 280.6 277.8 268.8 306.3 308.3 292.8 232.4

302.5 293.4 237.2 299.2 290.2 234.5 260.9 240.7 249.1 240.5 232.8 254.3 264.2 298.7 274.1 247.2 287.0 318.9 312.2 252.5 304.3

274.1 252.2 266.2 296.6 251.3 274.8 290.9

270.3

1. Measures of central tendency
2. Measures of variation
3. Measure of position
4. Shape of data distribution

Use rules of inference to show that the hypothesis "All lions are fierce","Some Lions do not drink coffee" imply the conclusion "Some fierce creatures do not drink coffee".

Nikbakht has received an email from an unknown mailer offering an entry into a lottery. For a price, he can get a ticket that may pay a prize double the price. He buys 2 tickets. Unknown to him an unfair system determines a winner where losing is two times more likely than winning. In what ways is this lottery unfair? What is the expected value of this lottery? In your estimation how much has he paid?

6. A risk neutral investor is considering insuring his assets worth 15000. These assets are subject to a random loss of 3 in 1000.

(a) What insurance premium can you offer him to buy?

(b) Are you able to ask for more? Explain fully why and how you may be able to ask for more.

Mr. Banabashi has a house, worth €180,000. He is concerned with earthquake risk and wishes to insure his property. It is known that either there is a rare chance of one in 10,000 of an earthquake causing the house to be destroyed completely. Or there is a more common chance of 1 in 100 of an earth trimmer causing discomfort.

His daughter, Bimianeh who is a student of ECO College of Insurance suggests his father should sell half share of his property and buy a half share of another property with equal earthquake risk. This, she argues will pool his risks. But she has difficulty convincing his father about this. They approach you for consultation.

(a) What would you say to them?

(b) Who do you think is right and why?