6. For each of the statements below, State whether it is true or false, and Motivate your answer with either a proof, a reference to a definition or theorem, or a counterexample. S:= T:= (a) Both and are spanning sets for R3. (b) Let vi Vk Vk+1,.Vn be vectors in a vector space V. Let S:={v1 V2., Vk) and T {Vk+1 Vk+2. Vn}. If S is linearly dependent, then SUT is linearly dependent. (c) If A is a (3 x 3) upper triangular matrix such that one of the diagonal entries of A is zero, then the column vectors of A are linearly dependent.

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…