Recent questions tagged goclasses-statistics-practice-questions

LET $X$ AND $Y$ BE TWO DISCRETE RANDOM VARIABLES WITH THE FOLLOWING JOINT PROBABILITY MASS FUNCTION (PMF):\begin{array}{lll}P(X, Y) & \mathrm{Y}=0 & \mathrm{Y}=1 \\\mathb...

LET $X$ BE A CONTINUOUS RANDOM VARIABLE CHOSEN UNIFORMLY AT RANDOM FROM THE INTERVAL $[0,5]$.LET $Y$ BE A NEW RANDOM VARIABLE DEFINED AS $Y=3 X+2$.WHAT IS THE VARIANCE, $...

A BIASSED COIN, FOR WHICH THE PROBABILITY OF LANDING HEADS IS $0.4$ , IS TOSSED $10$ TIMES. LET $X$ BE THE TOTAL NUMBER OF HEADS.WHAT IS THE VARIANCE, $\operatorname{Var}...

LET $X$ BE A CONTINUOUS RANDOM VARIABLE CHOSEN UNIFORMLY AT RANDOM FROM THE INTERVAL $[0,10]$.WHAT IS THE EXPECTED VALUE OF THE REMAINDER WHEN $X$ IS DIVIDED BY 3? (I.E.,...

YOU ROLL A FAIR SIX-SIDED DIE REPEATEDLY UNTIL A $6$ IS ROLLED. LET $S$ BE THE TOTAL SUM OF ALL OUTCOMES (INCLUDING THE FINAL $6$).WHAT IS THE EXPECTED VALUE, $E[S]$ ?$3....

A data analyst is studying the relationship between the number of study hours $(\mathrm{X})$ and the test scores $(\mathrm{Y})$ of $5$ students. The data is as follows:\[...

YOU ROLL A FAIR SIX-SIDED DIE. LET THE OUTCOME BE $N$. YOU THEN TOSS A FAIR COIN $N$ TIMES. LET $X$ BE THE TOTAL NUMBER OF HEADS.WHAT IS THE VARIANCE, $\operatorname{Var}...

LET $X$ BE AN EXPONENTIAL RANDOM VARIABLE WITH THE PROBABILITY DENSITY FUNCTION (P.D.F.) $f(x)=e^{-x}$ FOR $x \geq 0$.LET A NEW RANDOM VARIABLE $Y$ BE DEFINED AS $Y=X^2$....

YOU ROLL A FAIR SIX-SIDED DIE.IF THE RESULT IS EVEN, YOU DRAW A BALL FROM URN A. IF THE RESULT IS ODD, YOU DRAW A BALL FROM URN B. URN A CONTAINS $3$ BALLS MARKED "$10$" ...

AN URN CONTAINS $20$ DISTINCT BALLS, $5$ OF WHICH ARE WHITE AND $15$ ARE BLACK. YOU DRAW BALLS ONE BY ONE, WITHOUT REPLACEMENT. LET $X$ BE THE RANDOM VARIABLE REPRESENTIN...

A fair coin is flipped $10$ times. What is the expected number of "runs"? A run is a maximal consecutive sequence of identical outcomes. For example, the sequence $\text{...

Let $X$ and $Y$ be two random variables such that $\operatorname{Var}(X)=9, \operatorname{Var}(Y)=4$, and the variance of their difference, $\operatorname{Var}(X-Y)$, is ...

An urn contains $4$ Red balls and $6$ Blue balls ($10$ balls total). Two balls are drawn one after another without replacement.Let $X$ be an indicator variable that is $1...

Let $X_1, X_2, \ldots, X_{10}$ be the outcomes of 10 independent rolls of a single fair six-sided die. Let $S$ be the sum of these outcomes, $S=\sum_{i=1}^{10} X_i$. What...

A computer program receives a list of the $n$ distinct numbers $\{1,2, \ldots, n\}$ in a random order (i.e., all $n!$ permutations are equally likely). The program iterat...

The time $X$ (in minutes) a user spends on a website follows an exponential distribution with a mean of 0.5 minutes. The revenue $R$ generated from the user is a piecewis...

A loaded six-sided die has the following probability distribution for its outcome $X$ :$P(X=1)=0.1$ $P(X=2)=0.1$ $P(X=3)=0.1$ $P(X=4)=0.2$ $P(X=5)=0.2$ $P(X=6)=0.3$what i...

A university provost claims the average incoming student has an SAT score of $1200$. A researcher for the student newspaper is skeptical and believes the average score is...

A manufacturing process for engine pistons is specified to have a variance in piston diameter of $0.25 \mathrm{~mm}^2$. A new forging method is introduced, which is claim...

The standard deviation of a component in a drug is expected to be 0.00002 kg . A pharmacist suspecting the variability to be higher obtains a sample of 8 drugs and found ...

A new database query optimization algorithm is being tested. The old algorithm's mean execution time on a benchmark suite is 300 ms .A sample of 9 benchmark queries is ru...

A streaming service's data scientists know that $8 \%$ of users who visit a show's page will add it to their "Watchlist". After launching a new UI, they sample 2,000 user...

You keep tossing a fair coin until you see two consecutive heads (HH) for the first time. What is the expected number of tosses required?

Let $X_1, X_2, X_3$ be a random sample of size $3$ from a uniform distribution on the interval $[0,1]$.Let $Y=\max \left(X_1, X_2, X_3\right)$ be the maximum value in the...

A permutation $\pi=\left(\pi_1, \pi_2, \ldots, \pi_n\right)$ of the set $S=\{1,2, \ldots, n\}$ is chosen uniformly at random. A "fixed point" is defined as an index $i$ f...

Two distinct integers, $X$ and $Y$, are chosen at random without replacement from the set $S= \{1,2,3, \ldots, 100\}$.What is the variance of their sum, $\operatorname{Va...

In a class of 50 students, the number of students $n_i$ of each age $i$ is shown in the following table:\[\begin{array}{cr}\text{Age } (i) & n_i \\\hline18 & 20 \\19 & 22...

Two distinct integers, $X$ and $Y$, are chosen at random without replacement from the set $S= \{1,2,3, \ldots, 100\}$.What is the expected value of the smaller of the two...

The population standard deviation for the weight of 70-gram popcorn bags is claimed to be 2.5 grams. A random sample of 20 bags showed a sample standard deviation of 3 gr...

A car manufacturer advertises that its new model provides an average mileage of 40 km per litre. A consumer group is skeptical and believes the true mileage is less. To i...