MCQ's a. You know that the current rate of infection of COVID 19 is below 2% in NJ. Given that information, you are asked to infer the rate of infection of COVID in the US. This is a i. Predictive Analysis Task ii. Statistical analysis task iii. Probability calculation task b. Two events are mutually exclusive. i. They are dependent ii. They are independent iii. Could be either c. In a randomized trial with n=150, the goal is to randomize 70% to treatment and 30% to control. The number of people randomized to control is a random variable X. What is the probability distribution of X? i. Binomial (150, 0.7) ii. Normal (45, 5.61) iii. Binomial (150, 0.3) iv. None of the above
Addition Rule of Probability
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.
Expected Value
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 as the expectation, is denoted by: E(X).
Probability Distributions
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 choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
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 probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
MCQ's
a. You know that the current rate of infection of COVID 19 is below 2% in
NJ. Given that information, you are asked to infer the rate of infection of
COVID in the US. This is a
i. Predictive Analysis Task
ii. Statistical analysis task
iii.
b. Two events are mutually exclusive.
i. They are dependent
ii. They are independent
iii. Could be either
c. In a randomized trial with n=150, the goal is to randomize 70% to
treatment and 30% to control. The number of people randomized to
control is a random variable X. What is the probability distribution of
X?
i. Binomial (150, 0.7)
ii. Normal (45, 5.61)
iii. Binomial (150, 0.3)
iv. None of the above
d. Imagine rolling a fair dice 3 times and calculating the proportion p of
the rolls that result in the sum of the outcomes to be 10 after 3 rolls.
What is the probability of p?
e. Consider 4 independent events A1, A2, A3, A4. Let pi= P(Ai) denote
the probability of
of these four events occurs in terms of the pi’s.
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