Which property holds true for the cumulative distribution function (CDF) of a random variable X?
Show answer Hide answer
Answer: B. From smallest upto specific value of x
Explanation
By definition, cumulative distribution functions accumulate probability values continuously from the left side. This means they sum up all likelihoods starting from the absolute smallest possible outcome. The calculation stops precisely at the specified threshold value designated by the variable x. Probability theory uses cumulative distribution functions to completely describe real-valued random variables. The function value always ranges inclusively between zero and one for any valid input. It is a non-decreasing function that approaches one as the variable approaches positive infinity.
Engineers use cumulative probabilities to determine the likelihood of structural failure under load. Financial analysts apply these functions to calculate value at risk in investment portfolios. It helps decision makers understand the total probability of an event occurring below limits. Option a incorrectly suggests accumulating probabilities backward starting from larger values of x. Option c arbitrarily begins the accumulation at zero instead of the absolute smallest value. Option d is wrong because a valid standard mathematical definition is clearly provided here.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Which metric can never take a negative value (less than zero)?
Show answer Hide answer
Answer: B. Geometric Mean
The geometric mean relies strictly on positive numbers because negative roots yield complex or undefined values. Calculating this metric requires multiplying values together before extracting the nth root of that product...
Q2. What methods can be employed when testing for data randomness_____________?
Show answer Hide answer
Answer: C. Runs test
The runs test evaluates whether a sequence of data values occurs randomly. It analyzes the number of consecutive identical symbols or values in a series. Significant deviations from expected runs indicate non-random patt...
Q3. Which statistical measure does not use every observation ?
Show answer Hide answer
Answer: E. Mode
The mode identifies only the most frequent data point without calculating all values. Frequency counts determine the mode rather than numerical values of every observation. Entire portions of the dataset can change compl...
Q4. Which of the following represents a simple hypothesis___________________?
Show answer Hide answer
Answer: A. u = 20
A simple hypothesis specifies a single exact parameter value without leaving room for alternative conditions. Stating that the parameter equals twenty directly defines one precise point on the statistical distribution. R...
Q5. Which parameter dictates the relative flatness of a normal distribution curve?
Show answer Hide answer
Answer: C. Standard Deviation
The standard deviation controls the spread and dispersion of a normal curve. A larger standard deviation makes the bell curve wider and flatter. Conversely a smaller standard deviation makes the curve taller and narrower...
Q6. Which scenario is impossible during sampling ?
Show answer Hide answer
Answer: C. To make voters lists
Sampling is a standard procedure used to estimate population characteristics; it is not impossible to use.