Random Variables and Probability

Which of the following statements is NOT a characteristic of probabilities associated with a random variable?

A discrete random variable can take on any value within a given range, including fractional and decimal values.

What is the sum of all probabilities for all possible values of a discrete random variable?

For any random variable, $0 ≤ P(x) ≤ ______$, indicating that probabilities cannot exceed this value.

Match the random variables with their corresponding value types.

Which of the following real-world examples would be best represented by a continuous random variable, rather than a discrete one?

Define the expected value of a discrete random variable.

The variance of a discrete random variable can be negative.

Which of the following best describes the focus of Political Science according to the provided content?

Traditions are defined solely by material objects and possessions accumulated over time.

How does culture influence a society, according to the content provided?

According to the content, a ______ is an object, word, or action that stands for something else, without natural relationship, that is culturally defined.

Match each characteristic with its correct descriptor related to the concept of culture:

Which anthropological focus studies human origins, evolution, adaptation, and variation?

Which concept is described as the activity through which people make, preserve, and amend the general rules under which they live?

Customs are broad, abstract principles that guide thoughts and actions rather than specific practices.

Which of the following statements accurately describes a key property of the total area under a normal distribution curve?

In a standard normal distribution, the mean ($\mu$) is equal to 1 and the standard deviation ($\sigma$) is equal to 0.

What is the purpose of calculating a z-score?

A curve is said to be ______ to the x-axis if it approaches the x-axis but never actually touches or intersects it.

In the z-score formula for a sample, what does 's' represent?

Which of the following is the correct formula for calculating the z-score for a population?

A student scores 80 on a test where the mean is 70 and the standard deviation is 5. What is the student’s z-score?

Match the following terms with their corresponding definitions:

Which condition most directly contradicts the Hardy-Weinberg principle's assumption of random mating and equal embryo survival probability?

If a population splits due to vicariance, the newly isolated sub-populations are likely to maintain identical allele frequencies to the original population.

How might rare genes in a founding population impact the adaptation of organisms to a new isolated environment?

The evolutionary process where new species arise from a single ancestral species within the same geographic area is known as ______ speciation.

Match the following evolutionary mechanisms with their primary effect on population genetics:

Which of the following characteristics accurately describe plasmids used in gene cloning?

Polymerase Chain Reaction (PCR) is a manual method requiring constant researcher intervention to amplify specific DNA sequences.

What is the primary role of restriction enzymes in the process of gene isolation and cloning?

During PCR, the solution is ______ to break the hydrogen bonds between base pairs, causing the DNA double helix to open.

What is the role of DNA ligase in the context of recombinant DNA (rDNA) technology?

Match the following steps with their corresponding function in the PCR process:

In the context of gene cloning, what is a vector?

Briefly outline the three main steps involved in a standard Polymerase Chain Reaction (PCR) cycle.

Which of the following scenarios would most likely disrupt Hardy-Weinberg equilibrium in a population?

According to Lamarck's theory, acquired characteristics are inherited because genetic material changes in response to environmental pressures.

In the Hardy-Weinberg equation, what do the terms $p^2$, $2pq$, and $q^2$ represent?

Darwin's observations of distinct flora and fauna across different regions led him to realize that life forms ______ over time and vary from place to place.

Match the following concepts with their descriptions:

If a population of butterflies has two alleles for wing color, $B$ (dominant, black) and $b$ (recessive, white), and the frequency of the $b$ allele is 0.4, what is the frequency of the heterozygous genotype ($Bb$) assuming the population is in Hardy-Weinberg equilibrium?

Lamarck's theory of inheritance of acquired characteristics was ultimately rejected because:

In a population, the observed frequency of the homozygous recessive genotype is 0.04. Assuming Hardy-Weinberg equilibrium, what is the predicted frequency of the dominant allele?